Skip to main content Accessibility help
×
Hostname: page-component-84b7d79bbc-tsvsl Total loading time: 0 Render date: 2024-07-26T11:31:45.085Z Has data issue: false hasContentIssue false

References

Published online by Cambridge University Press:  20 September 2018

Neil M. Ribe
Affiliation:
Centre National de la Recherche Scientifique (CNRS), Paris
Get access

Summary

Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Chapter
Information
Publisher: Cambridge University Press
Print publication year: 2018

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Aharonov, E., Whitehead, J. A., Kelemen, P. B., and Spiegelman, M. 1995. Channeling instability of upwelling melt in the mantle. J. Geophys. Res., 100, 20, 433420, 450.Google Scholar
Albers, M., and Christensen, U. R. 2001. Channeling of plume flow beneath mid-ocean ridges. Earth Planet. Sci. Lett., 187, 207220.CrossRefGoogle Scholar
Androvandi, S. 2009. Convection multi-échelles à haut nombre de Rayleigh dans un fluide dont la viscosité dépend fortement de la température: Application au manteau terrestre. Ph.D. thesis, Institut de Physique du Globe de Paris, Paris, France.Google Scholar
Ansari, A., and Morris, S. 1985. The effects of a strongly temperature-dependent viscosity on Stokes’s drag law: experiments and theory. J. Fluid Mech., 159, 459476.Google Scholar
Asaadi, N., Ribe, N. M., and Sobouti, F. 2011. Inferring nonlinear mantle rheology from the shape of the Hawaiian swell. Nature, 473, 501504.CrossRefGoogle ScholarPubMed
Backus, G. E. 1958. A class of self-sustaining dissipative spherical dynamos. Ann. Phys., 4, 372447.CrossRefGoogle Scholar
Backus, G. E. 1967. Converting vector and tensor equations to scalar equations in spherical co-ordinates. Geophys. J. R. Astr. Soc., 13, 71101.Google Scholar
Bai, Q., Mackwell, S. J., and Kohlstedt, D. L. 1991. High-temperature creep of olivine single crystals, 1. Mechanical results for buffered samples. J. Geophys. Res., 96, 2441– 2463.Google Scholar
Barcilon, V., and Lovera, O. M. 1989. Solitary waves in magma dynamics. J. Fluid Mech., 204, 121133.Google Scholar
Barcilon, V., and Richter, F. M. 1986. Nonlinear waves in compacting media. J. Fluid Mech., 164, 429448.CrossRefGoogle Scholar
Barenblatt, G. I. 1996. Scaling, Self-Similarity, and Intermediate Asymptotics. Cambridge: Cambridge University Press.Google Scholar
Bassi, G., and Bonnin, J. 1988. Rheological modelling and deformation instability of lithosphere under extension. Geophys. J., 93, 485504.Google Scholar
Batchelor, G. K. 1967. An Introduction to Fluid Dynamics. Cambridge: Cambridge University Press.Google Scholar
Batchelor, G. K. 1970. Slender-body theory for particles of arbitrary cross-section in Stokes flow. J. Fluid Mech., 44, 419440.CrossRefGoogle Scholar
Bayly, B. 1982. Geometry of subducted plates and island arcs viewed as a buckling problem. Geology, 10, 629632.2.0.CO;2>CrossRefGoogle Scholar
Bellahsen, N., Faccenna, C., and Funiciello, F. 2005. Dynamics of subduction and plate motion in laboratory experiments: insights into the “plate tectonics” behavior of the Earth. J. Geophys. Res., 110, B01401.Google Scholar
Bercovici, D. 1993. A simple model of plate generation from mantle flow. Geophys. J. Int., 114, 635650.CrossRefGoogle Scholar
Bercovici, D. 1994. A theoretical model of cooling viscous gravity currents with temperature-dependent viscosity. Geophys. Res. Lett., 21, 11771180.Google Scholar
Bercovici, D. 1998. Generation of plate tectonics from lithosphere-mantle flow and void-volatile self-lubrication. Earth Planet. Sci. Lett., 154, 139151.Google Scholar
Bercovici, D., and Kelly, A. 1997. The non-linear initiation of diapirs and plume heads. Phys. Earth Planet. Int., 101, 119130.Google Scholar
Bercovici, D., and Lin, J. 1996. A gravity current model of cooling mantle plume heads with temperature-dependent buoyancy and viscosity. J. Geophys. Res., 101, 32913309.Google Scholar
Bercovici, D., and Long, M. D. 2014. Slab rollback instability and supercontinent dispersal. Geophys. Res. Lett., 41, 66596666.Google Scholar
Bercovici, D., and Ricard, Y. 2003. Energetics of a two-phase model of lithospheric damage, shear localization and plate-boundary formation. Geophys. J. Int., 152, 581596.CrossRefGoogle Scholar
Bercovici, D., Ricard, Y., and Schubert, G. 2001a. A two-phase model for compaction and damage 1. General theory. J. Geophys. Res., 106, 88878906.CrossRefGoogle Scholar
Bercovici, D., Ricard, Y., and Schubert, G. 2001b. A two-phase model for compaction and damage 3. Applications to shear localization and plate boundary formation. J. Geophys. Res., 106, 89258940.Google Scholar
Bercovici, D., and Rudge, J. F. 2016. A mechanism for mode selection in melt band instabilities. Earth Planet. Sci. Lett., 433, 139145.Google Scholar
Bercovici, D., Schubert, G., and Tackley, P. J. 1993. On the penetration of the 660 km phase change by mantle downflows. Geophys. Res. Lett., 20, 25992602.CrossRefGoogle Scholar
Bevis, M. 1986. The curvature of Wadati-Benioff zones and the torsional rigidity of subducting plates. Nature, 323, 5253.Google Scholar
Biot, M. A. 1954. Theory of stress-strain relations in anisotropic viscoelasticity and relaxation phenomena. J. Appl. Phys., 25, 13851391.Google Scholar
Blake, J. R. 1971. A note on the image system for a Stokeslet in a no-slip boundary. Proc. Camb. Phil. Soc., 70, 303310.Google Scholar
Bloor, M. I. G., and Wilson, M. J. 2006. An approximate analytic solution method for the biharmonic problem. Proc. R. Soc. Lond. A, 462, 11071121.Google Scholar
Bolton, E. W., and Busse, F. H. 1985. Stability of convection rolls in a layer with stress-free boundaries. J. Fluid Mech., 150, 487498.Google Scholar
Buckingham, E. 1914. On physically similar systems; illustrations of the use of dimensional equations. Phys. Rev., 4, 345376.Google Scholar
Buckmaster, J. D., Nachman, A., and Ting, L. 1975. The buckling and stretching of a viscida. J. Fluid Mech., 69, 120.Google Scholar
Budiansky, B., and Sanders, J. L. 1967. On the ‘best’ first-order linear shell theory. Pages 129140 of: W. Prager Anniversary Volume. New York: Macmillan.Google Scholar
Buffett, B. A. 2006. Plate force due to bending at subduction zones. J. Geophys. Res., 111, B09405.CrossRefGoogle Scholar
Buffett, B. A., and Becker, T. W. 2012. Bending stress and dissipation in subducted lithosphere. J. Geophys. Res., 117, B05413.Google Scholar
Buffett, B. A., Gable, C. W., and O’Connell, R. J. 1994. Linear stability of a layered fluid with mobile surface plates. J. Geophys. Res., 99, 19,885–19,900.Google Scholar
Busse, F. H. 1967a. On the stability of two-dimensional convection in a layer heated from below. J. Math. Phys., 46, 140150.Google Scholar
Busse, F. H. 1967b. The stability of finite amplitude cellular convection and its relation to an extremum principle. J. Fluid Mech., 30, 625649.CrossRefGoogle Scholar
Busse, F. H. 1981. On the aspect ratio of two-layer mantle convection. Phys. Earth Planet. Int., 24, 320324.Google Scholar
Busse, F. H. 1984. Instabilities of convection rolls with stress-free boundaries near threshold. J. Fluid Mech., 146, 115125.Google Scholar
Busse, F. H., and Frick, H. 1985. Square-pattern convection in fluids with strongly temperature-dependent viscosity. J. Fluid Mech., 150, 451465.CrossRefGoogle Scholar
Busse, F. H., Richards, M. A., and Lenardic, A. 2006. A simple model of high Prandtl and high Rayleigh number convection bounded by thin low-viscosity layers. Geophys. J. Int., 164, 160167.Google Scholar
Busse, F. H., and Schubert, G. 1971. Convection in a fluid with two phases. J. Fluid Mech., 46, 801812.Google Scholar
Butler, S. L. 2009. The effects of buoyancy on shear-induced melt bands in a compacting porous medium. Phys. Earth Planet. Int., 173, 5159.CrossRefGoogle Scholar
Butler, S. L. 2010. Porosity localizing instability in a compacting porous layer in a pure shear flow and the evolution of porosity band wavelength. Phys. Earth Planet. Int., 182, 3041.Google Scholar
Butler, S. L. 2012. Numerical models of shear-induced melt band formation with anisotropic matrix viscosity. Phys. Earth Planet. Int., 200201, 2836.Google Scholar
Butterworth, N. P., Quevedo, L., Morra, G., and Müller, R. D. 2012. Influence of overriding plate geometry and rheology on subduction. Geochem. Geophys. Geosyst., 13, Q06W15.Google Scholar
Caldwell, J. G., Haxby, W. F., Karig, D. E., and Turcotte, D. L. 1976. On the applicability of a universal elastic trench profile. Earth Planet. Sci. Lett., 31, 239246.Google Scholar
Canright, D., and Morris, S. 1993. Buoyant instability of a viscous film over a passive fluid. J. Fluid Mech., 255, 349372.CrossRefGoogle Scholar
Chandrasekhar, S. 1981. Hydrodynamic and Hydromagnetic Stability. New: Dover.Google Scholar
Čížková, H., and Bina, C. R. 2013. Effects of mantle and subduction-interface rheologies on slab stagnation and trench rollback. Earth Planet. Sci. Lett., 379, 95103.Google Scholar
Cloetingh, S., and Burov, E. 2011. Lithospheric folding and sedimentary basin evolution: a review and analysis of formation mechanisms. Basin Res., 23, 257290.Google Scholar
Connolly, J. A. D., and Podladchikov, Y. Y. 1998. Compaction-driven fluid flow in viscoelastic rock. Geodin. Acta, 11, 5584.CrossRefGoogle Scholar
Connolly, J. A. D., and Podladchikov, Y. Y. 2017. An analytical solution for solitary porosity waves: dynamic permeability and fluidization of nonlinear viscous and viscoplastic rock. Pages 285306 of: Gleeson, T., and Ingebritsen, S. E. (eds.), Crustal Permeability. Chichester: John Wiley & Sons, Ltd.Google Scholar
Conrad, C. P., and Molnar, P. 1997. The growth of Rayleigh-Taylor-type instabilities in the lithosphere for various rheological and density structures. Geophys. J. Int., 129, 95112.Google Scholar
Conrad, C. P., and Molnar, P. 1999. Convective instability of a boundary layer with temperature- and strain-rate-dependent viscosity in terms of ‘available buoyancy’. Geophys. J. Int., 139, 5168.CrossRefGoogle Scholar
Cox, R. G. 1970. The motion of long slender bodies in a viscous fluid Part 1. General theory. J. Fluid Mech., 44, 791810.Google Scholar
Crosby, A., and Lister, J. R. 2014. Creeping axisymmetric plumes with strongly temperature-dependent viscosity. J. Fluid Mech., 745, R2.Google Scholar
Dannberg, J., Eilon, Z., Faul, U., Gassmöller, R., Moulik, P., and Myhill, R. 2017. The importance of grain size to mantle dynamics and seismological observations. Geochem. Geophys. Geosyst., 18, 30343061.Google Scholar
Davaille, A. 1999. Two-layer thermal convection in miscible viscous fluids. J. Fluid Mech., 379, 223253.Google Scholar
Davaille, A., and Jaupart, C. 1994. Onset of thermal convection in fluids with temperature-dependent viscosity: application to the oceanic mantle. J. Geophys. Res., 99, 19,853– 19,866.Google Scholar
Davaille, A., and Limare, A. 2015. Laboratory studies of mantle convection. Pages 73144 of: Bercovici, D. (ed.), Treatise on Geophysics, 2nd edn., vol. 7. Amsterdam: Elsevier.Google Scholar
Davaille, A., and Vatteville, J. 2005. On the transient nature of mantle plumes. Geophys. Res. Lett., 32, L14309.Google Scholar
Drew, D. A., and Segel, L. A. 1971. Averaged equations for two-phase flows. Stud. Appl. Maths., 50, 205257.Google Scholar
Duretz, T., Schmalholz, S. M., and Gerya, T. V. 2012. Dynamics of slab detachment. Geochem. Geophys. Geosyst., 13, Q03020.Google Scholar
Dvorkin, J., Nur, A., Mavko, G., and Ben-Avraham, Z. 1993. Narrow subducting slabs and the origin of backarc basins. Tectonophys., 227, 6379.CrossRefGoogle Scholar
Dziewonski, A. M., and Anderson, D. L. 1981. Preliminary reference Earth model. Phys. Earth Planet. Int., 25, 297356.Google Scholar
Eckhaus, W. 1965. Studies in Non-Linear Stability Theory. Springer Tracts in Natural Philosophy, vol. 6. Berlin: Springer-Verlag.Google Scholar
England, P., and McKenzie, D. 1983. Correction to: a thin viscous sheet model for continental deformation. Geophys. J. R. Astr. Soc., 73, 523532.Google Scholar
Farrell, W. E. 1972. Deformation of the Earth by surface loads. Rev. Geophys. Space Phys., 10, 761797.Google Scholar
Feighner, M., and Richards, M. A. 1995. The fluid dynamics of plume-ridge and plume-plate interactions: an experimental investigation. Earth Planet. Sci. Lett., 129, 171182.Google Scholar
Fenner, R. T. 1975. On local solutions to non-Newtonian slow viscous flows. Int. J. Non-Linear Mech., 10, 207214.Google Scholar
Fleitout, L., and Froidevaux, C. 1983. Tectonic stresses in the lithosphere. Tectonics, 2, 315324.Google Scholar
Fletcher, C. A. J. 1984. Computational Galerkin Methods. New York: Springer.Google Scholar
Fletcher, R. C. 1974. Wavelength selection in the folding of a single layer with power-law rheology. Am. J. Sci., 274, 10291043.Google Scholar
Fletcher, R. C. 1977. Folding of a single viscous layer: exact infinitesimal-amplitude solution. Tectonophys., 39, 593606.Google Scholar
Fletcher, R. C., and Hallet, B. 1983. Unstable extension of the lithosphere: a mechanical model for Basin-and-Range structure. J. Geophys. Res., 88, 74577466.Google Scholar
Forte, A. M., and Mitrovica, J. X. 1996. A new inference of mantle viscosity based on a joint inversion of post-glacial rebound data and long-wavelength geoid anomalies. Geophys. Res. Lett., 23, 11471150.Google Scholar
Forte, A. M., Dziewonski, A. M., and Woodward, R. L. 1993. Aspherical structure of the mantle, tectonic plate motions, nonhydrostatic geoid, and topography of the core-mantle boundary. Pages 135166 of: Le Mouël, J.-L., Smylie, D. E., and Herring, T. (eds), Dynamics of the Earth’s Deep Interior and Earth Rotation. Geophys. Monogr., vol. 72. Washington: Am. Geophys. Union.Google Scholar
Forte, A. M., and Peltier, W. R. 1987. Plate tectonics and aspherical Earth structure: the importance of poloidal-toroidal coupling. J. Geophys. Res., 92, 36453679.CrossRefGoogle Scholar
Forte, A. M., and Peltier, W. R. 1991. Viscous flow models of global geophysical observables 1. Forward problems. J. Geophys. Res., 96, 20, 131–20, 159.Google Scholar
Forte, A. M., Peltier, W. R., and Dziewonski, A. M. 1991. Inferences of mantle viscosity from tectonic plate velocities. Geophys. Res. Lett., 18, 17471750.CrossRefGoogle Scholar
Fowler, A. C. 1985a. Fast thermoviscous convection. Stud. Appl. Maths., 72, 189219.Google Scholar
Fowler, A. C. 1985b. A mathematical model of magma transport in the asthenosphere. Geophys. Astrophys. Fluid Dyn., 33, 6396.Google Scholar
Fowler, A. C. 1990. A compaction model for melt transport in the Earth’s asthenosphere, part I, The basic model. Pages 314 of: Ryan, M. P. (ed.), Magma Transport and Storage. New York: John Wiley & Sons.Google Scholar
Fowler, A. C. 2011. Mathematical Geoscience. Berlin: Springer-Verlag.Google Scholar
Fowler, A. C., Howell, P. D., and Khaleque, T. S. 2016. Convection of a fluid with strongly temperature and pressure dependent viscosity. Geophys. Astrophys. Fluid Dyn., 110, 130165.Google Scholar
Frank, F. C. 1968. Curvature of island arcs. Nature, 220, 363.Google Scholar
Gantmacher, F. R. 1960. Matrix Theory. Vol. 1. Providence: AMS Chelsea Publishing.Google Scholar
Gavrilov, S. V., and Boiko, A. N. 2012. Waves in the diapir tail as a mechanism of hotspot pulsation. Izvestiya Phys. Solid Earth, 48, 550553.Google Scholar
Gebhardt, D. J., and Butler, S. L. 2016. Linear analysis of melt band formation in a mid-ocean ridge corner flow. Geophys. Res. Lett., 43, 37003707.Google Scholar
Gerardi, G., and Ribe, N. 2018. Boundary-element modeling of two-plate interaction at subduction zones: scaling laws and application to the Aleutian subduction zone. J. Geophys. Res. Solid Earth, 123, 52275248.Google Scholar
Goldenveizer, A. L. 1963. Derivation of an approximate theory of shells by means of asymptotic integration of the equations of the theory of elasticity. Prikl. Mat. Mech., 27, 593608.Google Scholar
Gomilko, A. M., Malyuga, V. S., and Meleshko, V. V. 2003. On steady Stokes flow in a trihedral rectangular corner. J. Fluid Mech., 476, 159177.Google Scholar
Gratton, J., and Minotti, F. 1990. Self-similar viscous gravity currents: phase-plane formalism. J. Fluid Mech., 210, 155182.Google Scholar
Gratton, J., Minotti, F., and Mahajan, S. M. 1999. Theory of creeping gravity currents of a non-Newtonian liquid. Phys. Rev. E, 60, 6960.Google Scholar
Green, A. E., and Zerna, W. 1992. Theoretical Elasticity. 2nd edn. Mineola: Dover.Google Scholar
Griffiths, R. W. 1986. Thermals in extremely viscous fluids, including the effects of temperature-dependent viscosity. J. Fluid Mech., 166, 115138.CrossRefGoogle Scholar
Griffiths, R. W., and Campbell, I. H. 1991. Interaction of mantle plume heads with the Earth’s surface and onset of small-scale convection. J. Geophys. Res., 96, 18,295– 18,310.Google Scholar
Grimshaw, R. H. J., Helfrich, K. R., and Whitehead, J. A. 1992. Conduit solitary waves in a visco-elastic medium. Geophys. Astrophys. Fluid Dyn., 65, 127147.Google Scholar
Hadamard, J. 1911. Mouvement permanent lent d’une sphère liquide et visqueuse dans un liquide visqueux. C. R. Acad. Sci. Paris, 152, 17351738.Google Scholar
Hager, B. H. 1984. Subducted slabs and the geoid: constraints on mantle rheology and flow. J. Geophys. Res., 89, 60036015.CrossRefGoogle Scholar
Hager, B. H., Clayton, R. W., Richards, M. A., Comer, R. P., and Dziewonski, A. M. 1985. Lower mantle heterogeneity, dynamic topography and the geoid. Nature, 313, 541545.Google Scholar
Hager, B. H., and O’Connell, R. J. 1979. Kinematic models of large-scale flow in the Earth’s mantle. J. Geophys. Res., 84, 10311048.Google Scholar
Hager, B. H., and O’Connell, R. J. 1981. A simple global model of plate tectonics and mantle convection. J. Geophys. Res., 86, 48434867.Google Scholar
Hager, B. H., and Richards, M. A. 1989. Long-wavelength variations in Earth’s geoid: physical models and dynamical implications. Phil. Trans. R. Soc. Lond. A, 328, 309327.Google Scholar
Happel, J., and Brenner, H. 1991. Low Reynolds Number Hydrodynamics. 2nd edn. Dordrecht: Kluwer Academic.Google Scholar
Harig, C., Molnar, P., and Houseman, G. A. 2008. Rayleigh–Taylor instability under a shear stress free top boundary condition and its relevance to removal of mantle lithosphere from beneath the Sierra Nevada. Tectonics, 27, TC6019.Google Scholar
Harris, S. 1996. Conservation laws for a nonlinear wave equation. Nonlinearity, 9, 187208.Google Scholar
Haskell, N. A. 1935. The motion of a viscous fluid under a surface load. Physics, 6, 265269.Google Scholar
Hauri, E. H., Whitehead, J. A. Jr, and Hart, S. R. 1994. Fluid dynamic and geochemical aspects of entrainment in mantle plumes. J. Geophys. Res., 99, 24,275–24,300.Google Scholar
Helmholtz, H. von. 1868. Zur Theorie der stationären Ströme in reibenden Flüssigkeiten. Verh. des naturh.-med. Vereins zu Heidelberg, 5, 17.Google Scholar
Hesse, M. A., Schiemenz, A. R., Liang, Y., and Parmentier, E. M. 2011. Compaction-dissolution waves in an upwelling mantle column. Geophys. J. Int., 187, 10571075.Google Scholar
Hewitt, I. J., and Fowler, A. C. 2009. Melt channelization in ascending mantle. J. Geophys. Res., 114, B06210.Google Scholar
Hier-Majumder, S., Ricard, Y., and Bercovici, D. 2006. Role of grain boundaries in magma migration and storage. Earth Planet. Sci. Lett., 248, 735749.Google Scholar
Hinch, E. J. 1991. Perturbation Methods. Cambridge: Cambridge University Press.Google Scholar
Höink, T., and Lenardic, A. 2010. Long wavelength convection, Poiseuille–Couette flow in the low-viscosity asthenosphere and the strength of plate margins. Geophys. J. Int., 180, 2333.Google Scholar
Holtzman, B. K., Groebner, N. J., Zimmerman, M. E., Ginsberg, S. B., and Kohlstedt, D. L. 2003. Stress-driven melt segregation in partially molten rocks. Geochem. Geophys. Geosyst., 4, 8607.Google Scholar
Houseman, G. A., and Molnar, P. 1997. Gravitational (Rayleigh–Taylor) instability of a layer with non-linear viscosity and convective thinning of continental lithosphere. Geophys. J. Int., 128, 125150.Google Scholar
Howard, L. N. 1964. Convection at high Rayleigh number. Pages 11091115 of: Görtler, H. (ed.), Proc. 11th Int. Congr. Appl. Mech. Berlin: Springer.Google Scholar
Hsui, A. T., and Tang, X.-M. 1988. A note on the weight and the gravitational torque of a subducting slab. J. Geodyn., 10, 18.Google Scholar
Hsui, A. T., Tang, X.-M., and Toksöz, M. N. 1990. On the dip angle of subducting plates. Tectonophys., 179, 163175.Google Scholar
Huppert, H. E. 1982. The propagation of two-dimensional and axisymmetric viscous gravity currents over a rigid horizontal surface. J. Fluid Mech., 121, 4358.Google Scholar
Husson, L., and Ricard, Y. 2004. Stress balance above subduction: application to the Andes. Earth Planet. Sci. Lett., 222, 10371050.CrossRefGoogle Scholar
Ismail-Zadeh, A., and Tackley, P. 2010. Computational Methods for Geodynamics. Cambridge: Cambridge University Press.Google Scholar
Ito, G. 2001. Reykjanes ‘V’-shaped ridges originating from a pulsing and dehydrating mantle plume. Nature, 411, 681684.Google Scholar
Jackson, J. D. 1975. Classical Electrodynamics. 2nd edn. New York: John Wiley & Sons.Google Scholar
Jarvis, G. T., and McKenzie, D. P. 1980. Convection in a compressible fluid with infinite Prandtl number. J. Fluid Mech., 96, 515583.Google Scholar
Jaupart, C., Molnar, P., and Cottrell, E. 2007. Instability of a chemically dense layer heated from below and overlain by a deep less viscous fluid. J. Fluid Mech., 572, 433469.Google Scholar
Jeffreys, H. 1930. The instability of a compressible fluid heated below. Proc. Camb. Phil. Soc., 26, 170172.Google Scholar
Jeong, J.-T., and Moffatt, H. K. 1992. Free-surface cusps associated with flow at low Reynolds number. J. Fluid Mech., 241, 122.Google Scholar
Jimenez, J., and Zufiria, J. A. 1987. A boundary-layer analysis of Rayleigh–Bénard convection at large Rayleigh number. J. Fluid Mech., 178, 5371.Google Scholar
Johnson, A. M., and Fletcher, R. C. 1994. Folding of Viscous Layers. New York: Columbia University Press.Google Scholar
Johnson, R. E. 1980. Slender-body theory for slow viscous flow. J. Fluid Mech., 75, 705714.Google Scholar
Kameyama, M. 2016. Linear analysis on the onset of thermal convection of highly compressible fluids with variable physical properties: implications for the mantle convection of super-Earths. Geophys. J. Int., 204, 11641178.Google Scholar
Kameyama, M., Miyagoshi, T., and Ogawa, M. 2015. Linear analysis on the onset of thermal convection of highly compressible fluids: implications for the mantle convection of super-Earths. Geophys. J. Int., 200, 10641075.Google Scholar
Katopodes, F. V., Davis, A. M. J., and Stone, H. A. 2000. Piston flow in a two-dimensional channel. Phys. Fluids, 12, 12401243.CrossRefGoogle Scholar
Katz, R. F., Spiegelman, M., and Holtzman, B. 2006. The dynamics of melt and shear localization in partially molten aggregates. Nature, 442, 676679.CrossRefGoogle ScholarPubMed
Kaufmann, G., and Lambeck, K. 2000. Mantle dynamics, postglacial rebound and the radial viscosity profile. Phys. Earth Planet. Int., 121, 303327.Google Scholar
Kaus, B. J. P., and Becker, T. W. 2007. Effects of elasticity on the Rayleigh–Taylor instability: implications for large-scale geodynamics. Geophys. J. Int., 168, 843862.Google Scholar
Ke, Y., and Solomatov, V. S. 2004. Plume formation in strongly temperature-dependent viscosity fluids over a very hot surface. Phys. Fluids, 16, 10591063.Google Scholar
Keller, J. B., and Rubinow, S. I. 1976. An improved slender-body theory for Stokes flow. J. Fluid Mech., 99, 411431.Google Scholar
Keller, T., and Katz, R. F. 2016. The role of volatiles in reactive melt transport in the asthenosphere. J. Petrol., 57, 10731108.Google Scholar
Kemp, D. V., and Stevenson, D. J. 1996. A tensile, flexural model for the initiation of subduction. Geophys. J. Int., 125, 7394.Google Scholar
Kerr, R. C., and Lister, J. R. 1987. The spread of subducted lithospheric material along the mid-mantle boundary. Earth Planet. Sci. Lett., 85, 241247.Google Scholar
Kevorkian, J., and Cole, J. D. 1996. Multiple Scale and Singular Perturbation Methods. New York: Springer.Google Scholar
Kim, M. C., and Choi, C. K. 2006. The onset of buoyancy-driven convection in fluid layers with temperature-dependent viscosity. Phys. Earth Planet. Int., 155, 4247.Google Scholar
Kim, S., and Karrila, S. J. 1991. Microhydrodynamics: Principles and Selected Applications. Boston: Butterworth-Heinemann.Google Scholar
King, S. D., and Masters, G. 1992. An inversion for radial viscosity structure using seismic tomography. Geophys. Res. Lett., 19, 15511554.Google Scholar
Koch, D. M., and Koch, D. L. 1995. Numerical and theoretical solutions for a drop spreading below a free fluid surface. J. Fluid. Mech., 287, 251278.Google Scholar
Koch, D. M., and Ribe, N. M. 1989. The effect of lateral viscosity variations on surface observables. Geophys. Res. Lett., 16, 535538.Google Scholar
Korenaga, J., and Jordan, T. H. 2003a. Physics of multiscale convection in Earth’s mantle: onset of sublithospheric convection. J. Geophys. Res., 108, 2333.Google Scholar
Korenaga, J., and Jordan, T. H. 2003b. Linear stability analysis of Richter rolls. Geophys. Res. Lett., 30, 2157.Google Scholar
Kraus, H. 1967. Thin Elastic Shells. New York: John Wiley & Sons.Google Scholar
Lachenbruch, A. H., and Nathenson, M. 1974. Rise of a variable viscosity fluid in a steadily spreading wedge-shaped conduit with accreting walls. Open File Rep. 74–251. U. S. Geol. Surv., Menlo Park, CA.Google Scholar
Ladyzhenskaya, O. A. 1963. The Mathematical Theory of Viscous Incompressible Flow. New York: Gordon and Breach.Google Scholar
Lamb, H. 1945. Hydrodynamics. New York: Dover.Google Scholar
Landau, L. D. 1944. On the problem of turbulence. C. R. Acad. Sci. U. R. S. S., 44, 311314.Google Scholar
Landau, L. D., and Lifshitz, E. 1986. Theory of Elasticity. 3rd edn. Oxford: Butterworth-Heinemann.Google Scholar
Landuyt, W., and Ierley, G. 2012. Linear stability analysis of the onset of sublithospheric convection. Geophys. J. Int., 189, 1928.Google Scholar
Langlois, W. E., and Deville, M. O. 2014. Slow Viscous Flow. New York: Springer.Google Scholar
Laravie, J. A. 1975. Geometry and lateral strain of subducted plates in island arcs. Geology, 3, 484486.Google Scholar
Larson, R. G. 1999. The Structure and Rheology of Complex Fluids. New York: Oxford University Press.Google Scholar
Leahy, G. M., and Bercovici, D. 2010. Reactive infiltration of hydrous melt above the mantle transition zone. J. Geophys. Res., 115, B08406.Google Scholar
Le Bars, M., and Davaille, A. 2002. Stability of thermal convection in two superimposed miscible viscous fluids. J. Fluid Mech., 471, 339363.Google Scholar
Le Bars, M., and Davaille, A. 2004. Large interface deformation in two-layer thermal convection of miscible viscous fluids. J. Fluid Mech., 499, 75110.Google Scholar
Lee, C., and King, S. 2011. Dynamic buckling of subducting slabs reconciles geological and geophysical observations. Earth Planet. Sci. Lett., 312, 360370.Google Scholar
Lee, E. H. 1955. Stress analysis in visco-elastic bodies. Quart. Appl. Math., 13, 183190.Google Scholar
Lee, S. H., and Leal, L. G. 1980. Motion of a sphere in the presence of a plane interface. Part 2. An exact solution in bipolar co-ordinates. J. Fluid Mech., 98, 193224.Google Scholar
Lemery, C., Ricard, Y., and Sommeria, J. 2000. A model for the emergence of thermal plumes in Rayleigh–Bénard convection at infinite Prandtl number. J. Fluid Mech., 414, 225250.Google Scholar
Lenardic, A., Richards, M. A., and Busse, F. H. 2006. Depth-dependent rheology and the horizontal length scale of mantle convection. J. Geophys. Res., 111, B07404.Google Scholar
Le Pichon, X., Francheteau, J., and Bonnin, J. 1973. Plate Tectonics. Amsterdam: Elsevier.Google Scholar
Lev, E., and Hager, B. H. 2008. Rayleigh–Taylor instabilities with anisotropic lithospheric viscosity. Geophys. J. Int., 173, 806814.Google Scholar
Li, Z., and Ribe, N. M. 2012. Dynamics of free subduction from 3-D boundary element modeling. J. Geophys. Res., 117, B06408.Google Scholar
Ligi, M., Cuffaro, M., Chierici, F., and Calafato, A. 2008. Three-dimensional passive mantle flow beneath mid-ocean ridges: an analytical approach. Geophys. J. Int., 175, 783805.Google Scholar
Lister, J. R., and Kerr, R. C. 1989a. The effect of geometry on the gravitiational instability of a region of viscous fluid. J. Fluid Mech., 202, 577594.Google Scholar
Lister, J. R., and Kerr, R. C. 1989b. The propagation of two-dimensional and axisymmetric viscous gravity currents at a fluid interface. J. Fluid Mech., 203, 215249.Google Scholar
Liu, X., and Zhong, S. 2013. Analyses of marginal stability, heat transfer and boundary layer properties for thermal convection in a compressible fluid with infinite Prandtl number. Geophys. J. Int., 194, 125144.Google Scholar
Longman, I. M. 1962. A Green’s function for determining the deformation of the earth under surface mass loads. J. Geophys. Res., 67, 845850.Google Scholar
Loper, D. E., and Stacey, F. D. 1983. The dynamical and thermal structure of deep mantle plumes. Phys. Earth Planet. Int., 33, 305317.Google Scholar
Lorentz, H. A. 1907. Ein allgemeiner Satz, die Bewegung einer reibenden Flüssigkeit betreffend, nebst einigen Anwendungen desselben. Abhand. Theor. Phys., 1, 2342.Google Scholar
Love, A. E. H. 1967. Some Problems of Geodynamics. New York: Dover.Google Scholar
Mahadevan, L., Bendick, R., and Liang, H. 2010. Why subduction zones are curved. Tectonics, 29, TC6002.Google Scholar
Maiden, M. D., and Hoefer, M. A. 2016. Modulations of viscous fluid conduit periodic waves. Proc. R. Soc. Lond. A, 472, 20160533.Google Scholar
Malkus, W. V. R., and Veronis, G. 1958. Finite amplitude cellular convection. J. Fluid Mech., 4, 225260.Google Scholar
Manga, M. 1996. Mixing of heterogeneities in the mantle: effect of viscosity differences. Geophys. Res. Lett., 23, 403406.Google Scholar
Manga, M. 1997. Interactions between mantle diapirs. Geophys. Res. Lett., 24, 18711874.Google Scholar
Manga, M., and Stone, H. A. 1993. Buoyancy-driven interaction between two deformable viscous drops. J. Fluid Mech., 256, 647683.Google Scholar
Manga, M., Stone, H. A., and O’Connell, R. J. 1993. The interaction of plume heads with compositional discontinuities in the earth’s mantle. J. Geophys. Res., 98, 19,979– 19,990.Google Scholar
Manga, M., Weeraratne, D., and Morris, S. J. S. 2001. Boundary-layer thickness and instabilities in Bénard convection of a liquid with a temperature-dependent viscosity. Phys. Fluids, 13, 802805.Google Scholar
Mangler, W. 1948. Zusammenhang zwischen ebenen und rotationssymmetrischen Grenzschichten in kompressiblen Flüssigkeiten. Z. Angew. Math. Mech., 28, 97103.Google Scholar
Marotta, A. M., and Mongelli, F. 1998. Flexure of subducted slabs. Geophys. J. Int., 132, 701711.Google Scholar
Marsh, B. D. 1978. On the cooling of ascending andesitic magma. Phil. Trans. R. Soc. Lond., 288, 611625.Google Scholar
Marsh, B. D., and Carmichael, I. S. E. 1974. Benioff zone magmatism. J. Geophys. Res., 79, 11961206.Google Scholar
McAdoo, D. C., Caldwell, J. G., and Turcotte, D. L. 1978. On the elastic-perfectly plastic bending of the lithosphere under generalized loading with application to the Kuril Trench. Geophys. J. R. Astr. Soc., 54, 1126.Google Scholar
McKenzie, D. 1988. The symmetry of convective transitions in space and time. J. Fluid Mech., 191, 287339.Google Scholar
McKenzie, D. P. 1967. Some remarks on heat flow and gravity anomalies. J. Geophys. Res., 72, 62616273.Google Scholar
McKenzie, D. P. 1969. Speculations on the consequences and causes of plate motions. Geophys. J. R. Astr. Soc., 18, 132.Google Scholar
McKenzie, D. P. 1977. Surface deformation, gravity anomalies and convection. Geophys. J. R. Astr. Soc., 48, 211238.Google Scholar
McKenzie, D. P. 1984. The generation and compaction of partially molten rock. J. Petrology, 25, 713765.Google Scholar
McKenzie, D. P., and Bowin, C. 1976. The relationship between bathymetry and gravity in the Atlantic ocean. J. Geophys. Res., 81, 19031915.Google Scholar
McKenzie, D. P., Roberts, J. M., and Weiss, N. O. 1974. Convection in the earth’s mantle: towards a numerical simulation. J. Fluid Mech., 62, 465538.Google Scholar
Medvedev, S. E., and Podladchikov, Y. Y. 1999. New extended thin-sheet approximation for geodynamic applications – I. Model formulation. Geophys. J. Int., 136, 567585.Google Scholar
Meleshko, V. V. 1996. Steady Stokes flow in a rectangular cavity. Proc. R. Soc. Lond. A, 452, 19992022.Google Scholar
Michaut, C., and Bercovici, D. 2009. A model for the spreading and compaction of two-phase viscous gravity currents. J. Fluid Mech., 630, 299329.Google Scholar
Mitrovica, J. X., and Forte, A. M. 2004. A new inference of mantle viscosity based upon joint inversion of convection and glacial isostatic adjustment data. Earth Planet. Sci. Lett., 225, 177189.Google Scholar
Mitrovica, J. X., Hay, C. C., Morrow, E., Kopp, R. E., Dumberry, M., and Stanley, S. 2015. Reconciling past changes in Earth’s rotation with 20th century global sea-level rise: resolving Munk’s enigma. Sci. Adv., 1, e1500679.Google Scholar
Mitrovica, J. X., and Peltier, W. R. 1995. Constraints on mantle viscosity based upon the inversion of post-glacial uplift data from the Hudson Bay region. Geophys. J. Int., 122, 353377.Google Scholar
Mittelstaedt, E., and Ito, G. 2005. Plume-ridge interaction, lithospheric stresses, and the origin of near-ridge volcanic lineaments. Geochem. Geophys. Geosyst., 6, Q06002.Google Scholar
Moffatt, H. K. 1964. Viscous and resistive eddies near a sharp corner. J. Fluid Mech., 18, 118.Google Scholar
Molnar, P., and Houseman, G. A. 2004. The effects of buoyant crust on the gravitational instability of thickened mantle lithosphere at zones of intracontinental convergence. Geophys. J. Int., 158, 11341150.Google Scholar
Molnar, P., and Houseman, G. A. 2013. Rayleigh–Taylor instability, lithospheric dynamics, surface topography at convergent mountain belts, and gravity anomalies. J. Geophys. Res. Solid Earth, 118, 25442557.Google Scholar
Molnar, P., and Houseman, G. A. 2015. Effects of a low-viscosity lower crust on topography and gravity at convergent mountain belts during gravitational instability of mantle lithosphere. J. Geophys. Res., 120, 537551.Google Scholar
Molnar, P., Houseman, G. A., and Conrad, C. P. 1998. Rayleigh–Taylor instability and convective thinning of mechanically thickened lithosphere: effects of non-linear viscosity decreasing exponentially with depth and of horizontal shortening of the layer. Geophys. J. Int., 133, 568584.Google Scholar
Mondal, P., and Korenaga, J. 2018. A propagator matrix method for the Rayleigh–Taylor instability of multiple layers: a case study on crustal delamination in the early Earth. Geophys. J. Int., 212, 18901901.Google Scholar
Morra, G., Chatelain, P., Tackley, P., and Koumoutsakos, P. 2007. Large scale three-dimensional boundary element simulation of subduction. Pages 1122–1129 of: Computational Science - ICCS 2007. New York: Springer.Google Scholar
Morra, G., Chatelain, P., Tackley, P., and Koumoutsakos, P. 2009. Earth curvature effects on subduction morphology: modeling subduction in a spherical setting. Acta Geotech., 4, 95105.Google Scholar
Morra, G., Quevedo, L., and Müller, R. D. 2012. Spherical dynamic models of top-down tectonics. Geochem Geophys Geosyst., 13, Q03005.Google Scholar
Morra, G., and Regenauer-Lieb, K. 2006. A coupled solid-fluid method for modelling subduction. Philos. Mag., 86, 33073323.Google Scholar
Morra, G., Regenauer-Lieb, K., and Giardini, D. 2006. Curvature of island arcs. Geology, 34, 877880.Google Scholar
Morris, S. 1980. An asymptotic method for determining the transport of heat and matter by creeping flows with strongly variable viscosity; fluid dynamic problems motivated by island arc volcanism. Ph.D. thesis, The Johns Hopkins University, Baltimore, MD.Google Scholar
Morris, S. 1982. The effects of a strongly temperature-dependent viscosity on slow flow past a hot sphere. J. Fluid Mech., 124, 126.Google Scholar
Morris, S., and Canright, D. 1984. A boundary-layer analysis of Bénard convection in a fluid of strongly temperature-dependent viscosity. Phys. Earth Planet. Int., 36, 355373.Google Scholar
Morris, S. J. S. 2008. Viscosity stratification and the horizontal scale of end-driven cellular flow. Phys. Fluids, 20, 063103.Google Scholar
Muskhelishvili, N. I. 1953. Some Basic Problems in the Mathematical Theory of Elasticity. Groningen: P. Noordhoff.Google Scholar
Nayfeh, A. 1973. Perturbation Methods. New York: John Wiley & Sons.Google Scholar
Neil, E. A., and Houseman, G. A. 1999. Rayleigh–Taylor instability of the upper mantle and its role in intraplate orogeny. Geophys. J. Int., 138, 89107.Google Scholar
Newell, A. C., Passot, T., and Lega, J. 1993. Order parameter equations for patterns. Ann. Rev. Fluid Mech., 25, 399453.Google Scholar
Newell, A. C., Passot, T., and Souli, M. 1990. The phase diffusion and mean drift equations for convection at finite Rayleigh numbers in large containers. J. Fluid Mech., 220, 187252.Google Scholar
Newell, A. C., and Whitehead, J. A. Jr. 1969. Finite bandwidth, finite amplitude convection. J. Fluid Mech., 38, 279303.Google Scholar
Niordson, F. I. 1985. Shell Theory. Amsterdam: North-Holland.Google Scholar
Nobili, C., and Otto, F. 2017. Limitations of the background field method applied to Rayleigh–Bénard convection. J. Math. Phys., 58, 093102.Google Scholar
Novozhilov, V. V. 1959. The Theory of Thin Shells. Groningen: Noordhoff.Google Scholar
Nyblade, A. A., and Sleep, N. H. 2003. Long lasting epeirogenic uplift from mantle plumes and the origin of the Southern African Plateau. Geochem. Geophys. Geosyst., 4, 1105.Google Scholar
O’Connell, R. J., Gable, C. W., and Hager, B. H. 1991. Toroidal-poloidal partitioning of lithospheric plate motion. Pages 535551 of: Sabadini, R. et al. (ed), Glacial Isostasy, Sea Level and Mantle Rheology. Dordrecht: Kluwer Academic.Google Scholar
Ohta, K., Yagi, T., Hirose, K., and Ohishi, Y. 2017. Thermal conductivity of ferropericlase in the Earth’s lower mantle. Earth Planet. Sci. Lett., 465, 2937.Google Scholar
Ohta, K., Yagi, T., Taketoshi, N., Hirose, K., Komabayashi, T., Baba, T., Ohishi, Y., and Hernlund, J. 2012. Lattice thermal conductivity of MgSiO3 perovskite and post-perovskite at the core–mantle boundary. Earth Planet. Sci. Lett., 349350, 109115.Google Scholar
Ohtani, E., Mizobata, H., Kudoh, Y., Nagase, T., Arashi, H., Yurimoto, H., and Miyagi, I. 1997. A new hydrous silicate, a water reservoir, in the upper part of the lower mantle. Geophys. Res. Lett., 24, 10471050.Google Scholar
Olson, P. 1990. Hot spots, swells and mantle plumes. Pages 3351 of: Ryan, M. P. (ed.), Magma Transport and Storage. New York: John Wiley & Sons.Google Scholar
Olson, P., and Christensen, U. 1986. Solitary wave propagation in a fluid conduit within a viscous matrix. J. Geophys. Res., 91, 63676374.Google Scholar
Olson, P., and Corcos, G. M. 1980. A boundary-layer model for mantle convection with surface plates. Geophys. J. R. Astr. Soc., 62, 195219.Google Scholar
Olson, P., and Singer, H. 1985. Creeping plumes. J. Fluid Mech., 158, 511531.Google Scholar
Olson, P., Schubert, G., and Anderson, C. 1993. Structure of axisymmetric mantle plumes. J. Geophys. Res., 98, 68296844.Google Scholar
Ortoleva, P., Chadam, J., Merino, E., and Sen, A. 1987. Geochemical self-organization II: the reactive-infiltration instability. Am. J. Sci., 287, 10081040.Google Scholar
Otto, F., and Seis, C. 2011. Rayleigh–Bénard convection: improved bounds on the Nusselt number. J. Math. Phys., 52, 083702.Google Scholar
Palm, E. 1960. On the tendency towards hexagonal cells in steady convection. J. Fluid Mech., 8, 183192.Google Scholar
Palm, E., Ellingsen, T., and Gjevik, B. 1967. On the occurrence of cellular motion in Bénard convection. J. Fluid Mech., 30, 651661.Google Scholar
Panasyuk, S. V., and Hager, B. H. 2000. Inversion for mantle viscosity profiles constrained by dynamic topography and the geoid, and their estimated errors. Geophys. J. Int., 143, 821836.Google Scholar
Parsons, B., and Daly, S. 1983. The relationship between surface topography, gravity anomalies, and the temperature structure of convection. J. Geophys. Res., 88, 1129– 1144.Google Scholar
Parsons, B., and McKenzie, D. 1978. Mantle convection and the thermal structure of the plates. J. Geophys. Res., 83, 44854496.Google Scholar
Parsons, B., and Molnar, P. 1976. The origin of outer topographic rises asssociated with trenches. Geophys. J. R. Astr. Soc., 45, 707712.Google Scholar
Pekeris, C. L. 1935. Thermal convection in the interior of the Earth. Mon. Not. R. Astr. Soc. Geophys. Suppl., 3, 343367.Google Scholar
Peltier, W. R. 1974. The impulse response of a Maxwell Earth. Rev. Geophys. Space Phys., 12, 649669.CrossRefGoogle Scholar
Peltier, W. R. 1989. Mantle viscosity. Pages 389478 of: Peltier, W. R. (ed.), Mantle Convection: Plate Tectonics and Global Dynamics. The Fluid Mechanics of Astrophysics and Geophysics, vol. 4. Montreux: Gordon and Breach.Google Scholar
Peltier, W. R. 1996. Mantle viscosity and ice-age ice sheet topography. Science, 273, 1359– 1364.Google Scholar
Peltier, W. R. 2004. Global glacial isostasy and the surface of the ice-age Earth: the ICE-5G (VM2) model and GRACE. Ann. Rev. Earth Planet. Sci., 32, 111149.Google Scholar
Peltier, W. R., Drummond, R. A., and Tushingham, A. M. 1986. Post-glacial rebound and transient lower mantle rheology. Geophys. J. R. Astr. Soc., 87, 79116.Google Scholar
Peltier, W. R., Jarvis, G. T., Forte, A. M., and Solheim, L. P. 1989. The radial structure of the mantle general circulation. Pages 765816 of: Peltier, W. R. (ed.), Mantle Convection: Plate Tectonics and Global Dynamics. The Fluid Mechanics of Astrophysics and Geophysics, vol. 4. Montreux: Gordon and Breach.Google Scholar
Peng, G. G., and Lister, J. R. 2014. The initial transient and approach to self-similarity of a very viscous buoyant thermal. J. Fluid Mech., 744, 352375.Google Scholar
Pozrikidis, C. 1990. The deformation of a liquid drop moving normal to a plane wall. J. Fluid Mech., 215, 331363.Google Scholar
Pozrikidis, C. 1992. Boundary Integral and Singularity Methods for Linearized Viscous Flow. Cambridge: Cambridge University Press.Google Scholar
Ramalho, R., Helffrich, G., Cosca, M., Vance, D., Hoffmann, D., and Schmidt, D. N. 2010. Episodic swell growth inferred from variable uplift of the Cape Verde hotspot islands. Nature Geosci., 3, 774777.Google Scholar
Rasenat, S., Busse, F. H., and Rehberg, I. 1989. A theoretical and experimental study of double-layer convection. J. Fluid Mech., 199, 519540.Google Scholar
Rayleigh, J. W. S. 1945. The Theory of Sound. 2nd edn. 2 vols. New York: Dover.Google Scholar
Renardy, Y., and Joseph, D. D. 1985. Oscillatory instability in a Bénard problem of two fluids. Phys. Fluids, 28, 788793.Google Scholar
Renardy, Y., and Renardy, M. 1985. Perturbation analysis of steady and oscillatory onset in a Bénard problem with two similar liquids. Phys. Fluids, 28, 26992708.Google Scholar
Ribe, N. M. 1989. Mantle flow induced by back-arc spreading. Geophys. J. R. Astr. Soc., 98, 8591.Google Scholar
Ribe, N. M. 1992. The dynamics of thin shells with variable viscosity and the origin of toroidal flow in the mantle. Geophys. J. Int., 110, 537552.Google Scholar
Ribe, N. M. 1998. Spouting and planform selection in the Rayleigh–Taylor instability of miscible viscous fluids. J. Fluid Mech., 234, 315336.Google Scholar
Ribe, N. M. 2001. Bending and stretching of thin viscous sheets. J. Fluid Mech., 433, 135160.Google Scholar
Ribe, N. M. 2002. A general theory for the dynamics of thin viscous sheets. J. Fluid Mech., 457, 255283.Google Scholar
Ribe, N. M. 2003. Periodic folding of viscous sheets. Phys. Rev. E, 68, 036305.Google Scholar
Ribe, N. M. 2010. Bending mechanics and mode selection in free subduction: a thin-sheet analysis. Geophys. J. Int., 180, 559576.Google Scholar
Ribe, N. M. 2015. Analytical approaches to mantle dynamics. Pages 145196 of: Schubert, G., and Bercovici, D. (eds.), Treatise on Geophysics, 2nd edn., vol. 7. Oxford: Elsevier.Google Scholar
Ribe, N. M., and Christensen, U. 1999. The dynamical origin of Hawaiian volcanism. Earth Planet. Sci. Lett., 171, 517531.Google Scholar
Ribe, N. M., Christensen, U. R., and Theissing, J. 1995. The dynamics of plume-ridge interaction, 1: Ridge-centered plumes. Earth Planet. Sci. Lett., 134, 155168.Google Scholar
Ribe, N. M., and Davaille, A. 2013. Dynamical similarity and density (non-) proportionality in experimental tectonics. Tectonophys., 608, 13711379.Google Scholar
Ribe, N. M., and Delattre, W. L. 1998. The dynamics of plume-ridge interaction-III. The effects of ridge migration. Geophys. J. Int., 133, 511518.Google Scholar
Ribe, N. M., Stutzmann, E., Ren, Y., and van der Hilst, R. 2007. Buckling instabilities of subducted lithosphere beneath the transition zone. Earth Planet. Sci. Lett., 254, 173179.Google Scholar
Ricard, Y. 2015. Physics of mantle convection. Pages 2371 of: Schubert, G., and Bercovici, D. (eds.), Treatise on Geophysics, 2nd. edn., vol. 7. Oxford: Elsevier.Google Scholar
Ricard, Y., Bercovici, D., and Schubert, G. 2001. A two-phase model for compaction and damage 2. Applications to compaction, deformation, and the role of interfacial surface tension. J. Geophys. Res., 106, 89078924.Google Scholar
Ricard, Y., Fleitout, L., and Froidevaux, C. 1984. Geoid heights and lithospheric stresses for a dynamic earth. Ann. Geophys., 2, 267286.Google Scholar
Ricard, Y., and Froidevaux, C. 1986. Stretching instabilities and lithospheric boudinage. J. Geophys. Res., 91, 83148324.Google Scholar
Ricard, Y., and Husson, L. 2005. Propagation of tectonic waves. Geophys. Res. Lett., 32, L17308.Google Scholar
Ricard, Y., Vigny, C., and Froidevaux, C. 1989. Mantle heterogeneities, geoid, and plate motion: a Monte Carlo inversion. J. Geophys. Res., 94, 13,739–13,754.Google Scholar
Richards, M. A., and Hager, B. H. 1984. Geoid anomalies in a dynamic Earth. J. Geophys. Res., 89, 59876002.Google Scholar
Richards, M. A., Hager, B. H., and Sleep, N. H. 1988. Dynamically supported geoid highs over hotspots: observation and theory. J. Geophys. Res., 93, 76907708.Google Scholar
Richardson, C. N., Lister, J. R., and McKenzie, D. 1996. Melt conduits in a viscous porous matrix. J. Geophys. Res., 101, 20,423–20,432.Google Scholar
Richter, F. M. 1973a. Convection and the large-scale circulation of the mantle. J. Geophys. Res., 78, 87358745.Google Scholar
Richter, F. M. 1973b. Dynamical models for sea floor spreading. Rev. Geophys. Space Phys., 11, 223287.Google Scholar
Richter, F. M., and Johnson, C. E. 1974. Stability of a chemically layered mantle. J. Geophys. Res., 79, 16351639.Google Scholar
Richter, F. M., and McKenzie, D. P. 1984. Dynamical models for melt segregation from a deformable matrix. J. Geol., 92, 729740.Google Scholar
Richter, F. M., and Parsons, B. 1975. On the interaction of two scales of convection in the mantle. J. Geophys. Res., 80, 25292541.Google Scholar
Roberts, G. O. 1979. Fast viscous Bénard convection. Geophys. Astrophys. Fluid Dyn., 12, 235272.Google Scholar
Roberts, P., Schubert, G., Zhang, K., Liao, X., and Busse, F. H. 2007. Instabilities in a fluid layer with phase changes. Phys. Earth Planet. Int., 165, 147157.Google Scholar
Royden, L. H., and Husson, L. 2006. Trench motion, slab geometry and viscous stresses in subduction systems. Geophys. J. Int., 167, 881905.Google Scholar
Rudge, J. F. 2014. Analytical solutions of compacting flow past a sphere. J. Fluid Mech., 746, 466497.Google Scholar
Rudge, J. F., and Bercovici, D. 2015. Melt-band instabilities with two-phase damage. Geophys. J. Int., 201, 640651.Google Scholar
Rudge, J. F., Bercovici, D., and Spiegelman, M. 2011. Disequilibrium melting of a two phase multicomponent mantle. Geophys. J. Int., 184, 699718.Google Scholar
Rudolph, M. L., Lekić, V., and Lithgow-Bertelloni, C. 2015. Viscosity jump in Earth’s mid-mantle. Science, 350, 13491352.Google Scholar
Runcorn, S. K. 1967. Flow in the mantle inferred from the low degree harmonics of the geopotential. Geophys. J. R. Astr. Soc., 14, 375384.Google Scholar
Rybczynski, W. 1911. Über die fortschreitende Bewegung einer flüssigen Kugel in einem zähen Medium. Bull. Int. Acad. Sci. Cracov., 1911A, 4046.Google Scholar
Sanchez-Palencia, E. 1990. Passages à la limite de l’élasticité tri-dimensionnelle à la théorie asymptotique des coques minces. C. R. Acad. Sci. Paris I, 309, 909916.Google Scholar
Sayag, R., and Worster, M. G. 2013. Axisymmetric gravity currents of power-law fluids over a rigid horizontal surface. J. Fluid Mech., 716, R5.Google Scholar
Schettino, A., and Tassi, L. 2012. Trench curvature and deformation of the subducting lithosphere. Geophys. J. Int., 188, 1834.Google Scholar
Schmalholz, S. M. 2011. A simple analytical solution for slab detachment. Earth Planet. Sci. Lett., 304, 4554.Google Scholar
Schmalholz, S. M., and Mancktelow, N. S. 2016. Folding and necking across the scales: a review of theoretical and experimental results and their applications. Solid Earth, 7, 14171465.Google Scholar
Schmeling, H. 2000. Partial melting and melt segregation in a convecting mantle. Pages 141178 of: Bagdassarov, N., Laporte, D., and Thompson, A. (eds.), Physics and Chemistry of Partially Molten Rocks. Norwell: Kluwer Academic.Google Scholar
Scholz, C. H., and Page, R. 1970. Buckling in island arcs. EOS (Am. Geophys. Union Trans.), 51, 429.Google Scholar
Schrank, C. E., Karrech, A., Boutelier, D. A., and Regenauer-Lieb, K. 2017. A comparative study of Maxwell viscoelasticity at large strains and rotations. Geophys. J. Int., 211, 252262.Google Scholar
Schubert, G., Olson, P., Anderson, C., and Goldman, P. 1989. Solitary waves in mantle plumes. J. Geophys. Res., 94, 95239532.Google Scholar
Schubert, G., and Turcotte, D. L. 1971. Phase changes and mantle convection. J. Geophys. Res., 76, 14241432.Google Scholar
Schubert, G., Turcotte, D. L., and Olson, P. 2001. Mantle Convection in the Earth and Planets. Cambridge: Cambridge University Press.Google Scholar
Schubert, G., Yuen, D. A., and Turcotte, D. L. 1975. Role of phase transitions in a dynamic mantle. Geophys. J. R. Astr. Soc., 42, 705735.Google Scholar
Scott, D. R., and Stevenson, D. J. 1984. Magma solitons. Geophys. Res. Lett., 11, 1161– 1164.Google Scholar
Scott, D. R., and Stevenson, D. J. 1986. Magma ascent by porous flow. J. Geophys. Res., 91, 92839296.Google Scholar
Scott, D. R., Stevenson, D. J., and Whitehead, J. A. Jr. 1986. Observations of solitary waves in a deformable pipe. Nature, 319, 759761.Google Scholar
Segel, L. 1969. Distant side-walls cause slow amplitude modulation of cellular convection. J. Fluid Mech., 38, 203224.Google Scholar
Shankar, P. N. 1993. The eddy structure in Stokes flow in a cavity. J. Fluid Mech., 250, 371383.Google Scholar
Shankar, P. N. 2005. Eigenfunction expansions on arbitrary domains. Proc. R. Soc. Lond. A, 461, 21212133.Google Scholar
Shiels, C., and Butler, S. L. 2015. Couette and Poiseuille flows in a low viscosity asthenosphere: effects of internal heating rate, Rayleigh number, and plate representation. Phys. Earth Planet. Int., 246, 3140.Google Scholar
Shishkina, O., Emran, M. S., Grossman, S., and Lohse, D. 2017. Scaling relations in large-Prandtl-number natural thermal convection. Phys. Rev. Fluids, 2, 103502.Google Scholar
Simpson, G., and Weinstein, M. I. 2008. Asymptotic stability of ascending solitary magma waves. SIAM J. Math. Anal., 40, 13371391.Google Scholar
Sleep, N. H. 1974. Segregation of a magma from a mostly crystalline mush. Bull. Geol. Soc. Am., 85, 12251232.Google Scholar
Sleep, N. H. 1987. Lithospheric heating by mantle plumes. Geophys. J. R. Astr. Soc., 91, 111.Google Scholar
Sleep, N. H. 1996. Lateral flow of hot plume material ponded at sublithospheric depths. J. Geophys. Res. Solid Earth, 101, 28,065–28,083.Google Scholar
Smith, R. B. 1975. Unified theory of the onset of folding, boudinage and mullion structure. Geol. Soc. Am. Bull., 86, 16011609.Google Scholar
Smith, R. B. 1977. Formation of folds, boudinage, and mullions in non-Newtonian materials. Geol. Soc. Am. Bull., 88, 312320.Google Scholar
Solomatov, V. S. 1995. Scaling of temperature- and stress-dependent viscosity convection. Phys. Fluids, 7, 266274.Google Scholar
Sotin, C., and Parmentier, E. M. 1989. On the stability of a fluid layer containing a univariant phase transition: application to planetary interiors. Phys. Earth Planet. Int., 55, 1025.Google Scholar
Sparrow, E. M., Husar, R. B., and Goldstein, R. J. 1970. Observations and other characteristics of thermals. J. Fluid Mech., 41, 793800.Google Scholar
Spiegelman, M. 1993. Flow in deformable porous media. Part 1 Simple analysis. J. Fluid Mech., 247, 1738.Google Scholar
Spiegelman, M. 2003. Linear analysis of melt band formation by simple shear. Geochem. Geophys. Geosyst., 4, 8615.Google Scholar
Spiegelman, M., Kelemen, P. B., and Aharonov, E. 2001. Causes and consequences of flow organization during melt transport: the reaction infiltration instability in compactible media. J. Geophys. Res., 106, 20612077.Google Scholar
Spiegelman, M., and McKenzie, D. 1987. Simple 2-D models for melt extraction at mid-ocean ridges and island arcs. Earth Planet. Sci. Lett., 83, 137152.Google Scholar
Šrámek, O., Ricard, Y., and Bercovici, D. 2007. Simultaneous melting and compaction in deformable two-phase media. Geophys. J. Int., 168, 964982.Google Scholar
Stengel, K. C., Oliver, D. S., and Booker, J. R. 1982. Onset of convection in a variable-viscosity fluid. J. Fluid Mech., 120, 411431.Google Scholar
Stevenson, D. J. 1989. Spontaneous small-scale melt segregation in partial melts undergoing deformation. Geophys. Res. Lett., 16, 10671070.Google Scholar
Stevenson, D. J., and Turner, J. S. 1977. Angle of subduction. Nature, 270, 334336.Google Scholar
Stimson, M., and Jeffrey, G. B. 1926. The motion of two spheres in a viscous fluid. Proc. R. Soc. Lond. A, 111, 110116.Google Scholar
Stokes, G. G. 1845. On the theories of the internal friction of fluids and of the equilibrium and motion of elastic solids. Trans. Camb. Phil. Soc., 8, 287347.Google Scholar
Stokes, G. G. 1851. On the effect of the internal friction of fluids on the motion of pendulums. Trans. Camb. Phil. Soc., 9, 199.Google Scholar
Straus, J. M. 1972. Finite amplitude doubly diffusive convection. J. Fluid Mech., 56, 353374.Google Scholar
Takei, Y., and Hier-Majumder, S. 2009. A generalized formulation of interfacial tension driven fluid migration with dissolution/precipitation. Earth Planet. Sci. Lett., 288, 138148.Google Scholar
Takei, Y., and Holtzman, B. K. 2009. Viscous constitutive relations of solid-liquid composites in terms of grain-boundary contiguity: 3. Causes and consequences of viscous anisotropy. J. Geophys. Res., 114, B06207.Google Scholar
Takei, Y., and Katz, R. F. 2013. Consequences of viscous anisotropy in a deforming, two-phase aggregate. Part 1. Governing equations and linearized analysis. J. Fluid Mech., 734, 424455.Google Scholar
Takei, Y., and Katz, R. F. 2015. Consequences of viscous anisotropy in a deforming, two-phase aggregate. Why is porosity-band angle lowered by viscous anisotropy? J. Fluid Mech., 784, 199224.Google Scholar
Tanimoto, T. 1997. Bending of a spherical lithosphere – axisymmetric case. Geophys. J. Int., 129, 305310.Google Scholar
Tanimoto, T. 1998. State of stress within a bending spherical shell and its implications for subducting lithosphere. Geophys. J. Int., 134, 199206.Google Scholar
Taylor-West, J., and Katz, R. F. 2015. Melt-preferred orientation, anisotropic permeability and melt-band formation in a deforming, partially molten aggregate. Geophys. J. Int., 203, 12531262.Google Scholar
Tovish, A., Schubert, G., and Luyendyk, B. P. 1978. Mantle flow pressure and the angle of subduction: non-Newtonian corner flows. J. Geophys. Res., 83, 58925898.Google Scholar
Turcotte, D. L. 1967. A boundary-layer theory for cellular convection. Int. J. Heat Mass Transfer, 10, 10651074.Google Scholar
Turcotte, D. L. 1974. Membrane tectonics. Geophys. J. R. Astr. Soc., 36, 3342.Google Scholar
Turcotte, D. L., McAdoo, D. C., and Caldwell, J. G. 1978. An elastic-perfectly plastic analysis of the bending of the lithosphere at a trench. Tectonophys., 47, 193205.Google Scholar
Turcotte, D. L., and Oxburgh, E. R. 1967. Finite amplitude convection cells and continental drift. J. Fluid Mech., 28, 2942.Google Scholar
Turcotte, D. L., and Schubert, G. 2014. Geodynamics. 3rd edn. Cambridge: Cambridge University Press.Google Scholar
Turcotte, D. L., Willemann, R. J., Haxby, W. W., and Norberry, J. 1981. Role of membrane stresses in the support of planetary topography. J. Geophys. Res., 86, 39513959.Google Scholar
Umemura, A., and Busse, F. H. 1989. Axisymmetric convection at large Rayleigh number and infinite Prandtl number. J. Fluid Mech., 208, 459478.Google Scholar
Van Ark, E., and Lin, J. 2004. Time variation in igneous volume flux of the Hawaii-Emperor hot spot seamount chain. J. Geophys. Res., 109, B11401.Google Scholar
Van Dyke, M. 1975. Perturbation Methods in Fluid Mechanics. Stanford: Parabolic Press.Google Scholar
Vasilyev, O. V., Ten, A. A., and Yuen, D. A. 2001. Temperature-dependent viscous gravity currents with shear heating. Phys. Fluids, 13, 36643674.Google Scholar
Vermeersen, L. L. A., and Sabadini, R. 1997. A new class of stratified viscoelastic models by analytical techniques. Geophys. J. Int., 129, 531570.Google Scholar
Vidal, V., and Bonneville, A. 2004. Variations of the Hawaiian hot spot activity revealed by variations in the magma production rate. J. Geophys. Res., 109, B03104.Google Scholar
von Mises, R. 1927. Bemerkungen zur Hydrodynamik. Z. Angew. Math. Mech., 7, 425431.Google Scholar
Vynnycky, M., and Masuda, Y. 2013. Rayleigh–Bénard convection at high Rayleigh number and infinite Prandtl number: asymptotics and numerics. Phys. Fluids, 25, 113602.Google Scholar
Wakiya, S. 1975. Application of bipolar coordinates to the two-dimensional creeping motion of a liquid. II. Some problems for two circular cylinders in viscous fluid. J. Phys. Soc. Japan, 39, 16031607.Google Scholar
Watts, A. B. 1978. An analysis of isostasy in the world’s oceans 1. Hawaiian-Emperor Seamount Chain. J. Geophys. Res., 83, 59896004.Google Scholar
Watts, A. B. 2001. Isostasy and Flexure of the Lithosphere. Cambridge: Cambridge University Press.Google Scholar
Watts, A. B., and Talwani, M. 1974. Gravity anomalies seaward of deep-sea trenches and their tectonic implications. Geophys. J. R. Astr. Soc., 36, 5790.Google Scholar
Wdowinski, S., O’Connell, R. J., and England, P. 1989. A continuum model of continental deformation above subduction zones: application to the Andes and the Aegean. J. Geophys. Res., 94, 10,331–10,346.Google Scholar
Weinstein, S. A., and Olson, P. L. 1992. Thermal convection with non-Newtonian plates. Geophys. J. Int., 111, 515530.Google Scholar
Wessel, P. 1996. Analytical solutions for 3-D flexural deformation of semi-infinite elastic plates. Geophys. J. Int., 124, 907918.Google Scholar
White, D. B. 1981. Experiments with convection in a variable viscosity fluid. Ph.D. thesis, University of Cambridge.Google Scholar
White, D. B. 1988. The planforms and onset of convection with a temperature-dependent viscosity. J. Fluid Mech., 191, 247286.Google Scholar
Whitehead, J. A. Jr., Dick, H. B. J., and Schouten, H. 1984. A mechanism for magmatic accretion under spreading centers. Nature, 312, 146148.Google Scholar
Whitehead, J. A. Jr., and Helfrich, K. R. 1986. The Korteweg-de Vries equation from laboratory conduit and magma migration equations. Geophys. Res. Lett., 13, 545546.Google Scholar
Whitehead, J. A. Jr., and Helfrich, K. R. 1988. Wave transport of deep mantle material. Nature, 335, 5961.Google Scholar
Whitehead, J. A. Jr., and Luther, D. S. 1975. Dynamics of laboratory diapir and plume models. J. Geophys. Res., 80, 705717.Google Scholar
Whitham, G. B. 1974. Linear and Non-Linear Waves. Sydney: Wiley-Interscience.Google Scholar
Whittaker, R. J., and Lister, J. R. 2006a. Steady axisymmetric creeping plumes above a planar boundary. Part 1. A point source. J. Fluid Mech., 567, 361378.Google Scholar
Whittaker, R. J., and Lister, J. R. 2006b. Steady axisymmetric creeping plumes above a planar boundary. Part 2. A distributed source. J. Fluid Mech., 567, 379397.Google Scholar
Whittaker, R. J., and Lister, J. R. 2008a. The self-similar rise of a buoyant thermal in very viscous flow. J. Fluid Mech., 606, 295324.Google Scholar
Whittaker, R. J., and Lister, J. R. 2008b. Slender-body theory for steady sheared plumes in very viscous fluid. J. Fluid Mech., 612, 2144.Google Scholar
Wiggins, C., and Spiegelman, M. 1993. Magma migration and magmatic solitary waves in 3-D. Geophys. Res. Lett., 22, 12891292.Google Scholar
Willemann, R. J., and Davies, G. F. 1982. Bending stresses in subducted lithosphere. Geophys. J. R. Astr. Soc., 71, 215224.Google Scholar
Worster, M. G. 1986. The axisymmetric laminar plume: asymptotic solution for large Prandtl number. Stud. Appl. Maths., 75, 139152.Google Scholar
Xu, B., and Ribe, N. M. 2016. A hybrid boundary-integral/thin-sheet equation for subduction modelling. Geophys. J. R. Astr. Soc., 206, 15521562.Google Scholar
Yale, M. M., and Phipps Morgan, J. 1998. Asthenosphere flow model of hotspot-ridge interactions: a comparison of Iceland and Kerguelen. Earth Planet. Sci. Lett., 161, 4556.Google Scholar
Yamazaki, D., and Karato, S.-I. 2001. Some mineral physics constraints on the rheology and geothermal structure of Earth’s lower mantle. Am. Mineralogist, 86, 385391.Google Scholar
Yarushina, V. M., and Podladchikov, Y. Y. 2015. (De)compaction of porous viscoelastoplastic media: model formulation. J. Geophys. Res. Solid Earth, 120, 41464170.Google Scholar
Yarushina, V. M., Podladchikov, Y. Y., and Connolly, J. A. D. 2015. (De)compaction of porous viscoelastoplastic media: solitary porosity waves. J. Geophys. Res. Solid Earth, 120, 48434862.Google Scholar
Yuen, D. A., and Schubert, G. 1976. Mantle plumes: a boundary-layer approach for Newtonian and non-Newtonian temperature-dependent rheologies. J. Geophys. Res., 81, 24992510.Google Scholar
Zhong, S. 1996. Analytic solutions for Stokes’ flow with lateral variations in viscosity. Geophys. J. Int., 124, 1828.Google Scholar

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

  • References
  • Neil M. Ribe, Centre National de la Recherche Scientifique (CNRS), Paris
  • Book: Theoretical Mantle Dynamics
  • Online publication: 20 September 2018
Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

  • References
  • Neil M. Ribe, Centre National de la Recherche Scientifique (CNRS), Paris
  • Book: Theoretical Mantle Dynamics
  • Online publication: 20 September 2018
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • References
  • Neil M. Ribe, Centre National de la Recherche Scientifique (CNRS), Paris
  • Book: Theoretical Mantle Dynamics
  • Online publication: 20 September 2018
Available formats
×