Skip to main content Accessibility help
×
Home

A settling-driven instability in two-component, stably stratified fluids

  • A. Alsinan (a1), E. Meiburg (a1) and P. Garaud (a2)

Abstract

We analyse the linear stability of stably stratified fluids whose density depends on two scalar fields where one of the scalar fields is unstably stratified and involves a settling velocity. Such conditions may be found, for example, in flows involving the transport of sediment in addition to heat or salt. A linear stability analysis for constant-gradient base states demonstrates that the settling velocity generates a phase shift between the perturbation fields of the two scalars, which gives rise to a novel, settling-driven instability mode. This instability mechanism favours the growth of waves that are inclined with respect to the horizontal. It is active for all density and diffusivity ratios, including for cases in which the two scalars diffuse at identical rates. If the scalars have unequal diffusivities, it competes with the elevator mode waves of the classical double-diffusive instability. We present detailed linear stability results as a function of the governing dimensionless parameters, including for lateral gradients of the base state density fields that result in predominantly horizontal intrusion instabilities. Highly resolved direct numerical simulation results serve to illustrate the nonlinear competition of the various instabilities for such flows in different parameter regimes.

Copyright

Corresponding author

Email address for correspondence: meiburg@engineering.ucsb.edu

References

Hide All
Alldredge, A. & Cohen, Y. 1987 Can microscale chemical patches persist in the sea? Microelectrode study of marine snow, fecal pellets. Science 235 (4789), 689691.
Baines, P. G. & Gill, A. E. 1969 On thermohaline convection with linear gradients. J. Fluid Mech. 37, 289306.
Burns, P. & Meiburg, E. 2012 Sediment-laden fresh water above salt water: linear stability analysis. J. Fluid Mech. 691, 279314.
Burns, P. & Meiburg, E. 2015 Sediment-laden fresh water above salt water: nonlinear simulations. J. Fluid Mech. 762, 156195.
Carazzo, G. & Jellinek, A. M. 2013 Particle sedimentation and diffusive convection in volcanic ash-clouds. J. Geophys. Res. 118 (4), 14201437.
Carey, S. 1997 Influence of convective sedimentation on the formation of widespread tephra fall layers in the deep sea. Geology 25 (9), 839842.
Chen, C. F. 1997 Particle flux through sediment fingers. Deep-Sea Res. I 44 (9), 16451654.
Davarpanah, J. S. & Wells, M. G. 2016 Enhanced sedimentation beneath particle-laden flows in lakes and the ocean due to double-diffusive convection. Geophys. Res. Lett. 43 (20), 1088310890.
Green, T. 1987 The importance of double diffusion to the settling of suspended material. Sedimentology 34 (2), 319331.
Green, T. & Diez, T. 1995 Vertical plankton transport due to self-induced convection. J. Plankton Res. 17 (9), 17231730.
Holyer, J. Y. 1983 Double-diffusive interleaving due to horizontal gradients. J. Fluid Mech. 137, 347362.
Hoyal, D., Bursik, M. & Atkinson, J. 1999a The influence of diffusive convection on sedimentation from buoyant plumes. Mar. Geol. 159 (1), 205220.
Hoyal, D., Bursik, M. & Atkinson, J. 1999b Settling-driven convection: a mechanism of sedimentation from stratified fluids. J. Geophys. Res. 104 (C4), 79537966.
Lampitt, R., Achterberg, E., Anderson, T., Hughes, J. A., Iglesias-Rodriguez, M. D., Kelly-Gerreyn, B. A., Lucas, M., Popova, E. E., Sanders, R., Shepherd, J. G. et al. 2008 Ocean fertilization: a potential means of geoengineering? Phil. Trans. R. Soc. Lond. A 366 (1882), 39193945.
Lele, S. K. 1992 Compact finite difference schemes with spectral-like resolution. J. Comput. Phys. 103 (1), 1642.
Manville, V. & Wilson, C. J. N. 2004 Vertical density currents: a review of their potential role in the deposition and interpretation of deep-sea ash layers. J. Geol. Soc. 161 (6), 947958.
Manzella, I., Bonadonna, C., Phillips, J. C. & Monnard, H. 2015 The role of gravitational instabilities in deposition of volcanic ash. Geology 43 (3), 211214.
Maxworthy, T. 1999 The dynamics of sedimenting surface gravity currents. J. Fluid Mech. 392, 2744.
Medrano, M., Garaud, P. & Stellmach, S. 2014 Double-diffusive mixing in stellar interiors in the presence of horizontal gradients. Astrophys. J. Lett. 792 (2), L30.
Parsons, J., Bush, J. & Syvitski, J. 2001 Hyperpycnal plume formation from riverine outflows with small sediment concentrations. Sedimentology 48 (2), 465478.
Parsons, J. & García, M. 2000 Enhanced sediment scavenging due to double-diffusive convection. Intl J. Sedim. Res. 70 (1), 4752.
Radko, T. 2013 Double-diffusive Convection. Cambridge University Press.
Reali, J. F., Garaud, P., Alsinan, A. & Meiburg, E. 2017 Layer formation in sedimentary fingering convection. J. Fluid Mech. 816, 268305.
Rouhnia, M. & Strom, K. 2015 Sedimentation from flocculated suspensions in the presence of settling-driven gravitational interface instabilities. J. Geophys. Res. 120 (9), 63846404.
Ruddick, B. R. & Turner, J. S. 1979 The vertical length scale of double-diffusive intrusions. Deep-Sea Res. A 26 (8), 903913.
Sánchez, X. & Roget, E. 2007 Microstructure measurements and heat flux calculations of a triple-diffusive process in a lake within the diffusive layer convection regime. J. Geophys. Res. 112 (C2), C02012.
Scheu, K. R., Fong, D. A., Monismith, S. G. & Fringer, O. B. 2015 Sediment transport dynamics near a river inflow in a large alpine lake. Limnol. Oceanogr. 60 (4), 11951211.
Schulte, B., Konopliv, N. & Meiburg, E. 2016 Clear salt water above sediment-laden fresh water: Interfacial instabilities. Phys. Rev. Fluids 1 (1), 012301.
Segre, P. N., Liu, F., Umbanhowar, P. & Weitz, D. A. 2001 An effective gravitational temperature for sedimentation. Nature (London) 409, 594.
Stern, M. E. 1960 The salt-fountain and thermohaline convection. Tellus 12 (2), 172175.
Stern, M. E. 1967 Lateral mixing of water masses. In Deep Sea Research and Oceanographic Abstracts, vol. 14, pp. 747753. Elsevier.
Turner, J. S. 1979 Buoyancy Effects in Fluids. Cambridge University Press.
Turner, J. S. 1985 Multicomponent convection. Annu. Rev. Fluid Mech. 17 (1), 1144.
Williamson, J. H. 1980 Low-storage Runge–Kutta schemes. J. Comput. Phys. 35 (1), 4856.
Yu, X., Hsu, T. & Balachandar, S. 2013 Convective instability in sedimentation: linear stability analysis. J. Geophys. Res. 118 (1), 256272.
Yu, X., Hsu, T. & Balachandar, S. 2014 Convective instability in sedimentation: 3-d numerical study. J. Geophys. Res. 119 (11), 81418161.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

JFM classification

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed