Hostname: page-component-7c8c6479df-xxrs7 Total loading time: 0 Render date: 2024-03-28T17:52:03.470Z Has data issue: false hasContentIssue false

Channel formation by turbidity currents: Navier–Stokes-based linear stability analysis

Published online by Cambridge University Press:  25 November 2008

B. HALL
Affiliation:
Department of Mechanical Engineering, University of California, Santa Barbara, CA 93106, USA
E. MEIBURG*
Affiliation:
Department of Mechanical Engineering, University of California, Santa Barbara, CA 93106, USA
B. KNELLER
Affiliation:
Department of Geology and Petroleum Geology, University of Aberdeen, Aberdeen AB24 3FX, UK
*
Author to whom correspondence should be addressed: meiburg@engineering.ucsb.edu

Abstract

The linear stability of an erodible sediment bed beneath a turbidity current is analysed, in order to identify potential mechanisms responsible for the formation of longitudinal gullies and channels. On the basis of the three-dimensional Navier–Stokes equations, the stability analysis accounts for the coupled interaction of the three-dimensional fluid and particle motion inside the current with the erodible bed below it. For instability to occur, the suspended sediment concentration of the base flow needs to decay away from the sediment bed more slowly than does the shear stress inside the current. Under such conditions, an upward protrusion of the sediment bed will find itself in an environment where erosion decays more quickly than sedimentation, and so it will keep increasing. Conversely, a local valley in the sediment bed will see erosion increase more strongly than sedimentation, which again will amplify the initial perturbation.

The destabilizing effect of the base flow is modulated by the stabilizing perturbation of the suspended sediment concentration and by the shear stress due to a secondary flow structure in the form of counter-rotating streamwise vortices. These streamwise vortices are stabilizing for small Reynolds and Péclet numbers and destabilizing for large values.

For a representative current height of O(10–100m), the linear stability analysis provides the most amplified wavelength in the range of 250–2500m, which is consistent with field observations reported in the literature. In contrast to previous analyses based on depth-averaged equations, the instability mechanism identified here does not require any assumptions about sub- or supercritical flow, nor does it require the presence of a slope or a slope break.

Type
Papers
Copyright
Copyright © Cambridge University Press 2008

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

REFERENCES

Altinakar, M. S., Graf, W. H. & Hopfinger, E. J. 1996 Flow structure in turbidity currents. J. Hydraul. Res. 34, 713718.CrossRefGoogle Scholar
Birman, V. K., Martin, J. E. & Meiburg, E. 2005 The non-Boussinesq lock-exchange problem. Part 2. High-resolution simulations. J. Fluid Mech. 537, 125144.CrossRefGoogle Scholar
Birnir, B., Smith, T. R. & Merchant, G. E. 2001 The scaling of fluvial landscapes. Comput. Geosci. 27, 12171230.CrossRefGoogle Scholar
Blanchette, F., Strauss, M., Meiburg, E., Kneller, B. & Glinsky, M. E. 2005 High resolution numerical simulations of resuspending gravity currents: conditions for self-sustainment. J. Geophys. Res. C: 110, C12022, doi:10.1029/2005JC002927.CrossRefGoogle Scholar
Bloneaux, P. 2001 Mechanics of coastal forms. Annu. Rev. Fluid Mech. 33, 339370.Google Scholar
Bosse, T., Kleiser, L. & Meiburg, E. 2006 Small particles in homogeneous turbulence: settling velocity enhancement by two-way coupling. Phys. Fluids 18, 027102.CrossRefGoogle Scholar
Campbell, D. C., Shimeld, J. W., Mosher, D. C. & Piper, D. J. W. 2004 Relationships between sediment mass failure modes and magnitudes in the evolution of the Scotian Slope, offshore Nova Scotia. In Offshore Technology Conference, Houston, Texas, Paper 16743.Google Scholar
Chikita, K. 1989 A field study of turbidity currents initiated by spring run-offs. Water Resour. Res. 25, 257271.Google Scholar
Chikita, K. 1990 Sedimentation by river-induced turbidity currents: field measurements and interpretation. Sedimentology 37, 891905.Google Scholar
Choux, C. M. A., Baas, J. H., McCaffrey, W. D. & Haughton, P. D. W. 2005 Comparison of spatio-temporal evolution of experimental particulate gravity flows at two different initial concentrations, based on velocity, grain size and density data. Sedim. Geol. 179, 4969.Google Scholar
Colombini, M. 1993 Turbulence-driven secondary flows and formation of sand ridges. J. Fluid Mech. 254, 701719.Google Scholar
Colombini, M. & Parker, G. 1995 Longitudinal streaks. J. Fluid Mech. 304, 161183.CrossRefGoogle Scholar
Driscoll, N. W., Weissel, J. K. & Goff, J. A. 2000 Potential for large-scale submarine slope failure and tsunami generation along the U.S. mid-Atlantic coast. Geology 28 (5), 407410.2.0.CO;2>CrossRefGoogle Scholar
Engelund, F. 1964 A practical approach to self-preserving turbulent flows. Acta Polytechnica Scandinavica, Civil Engineering and Building Construction Series 27, 6.Google Scholar
Etienne, J., Hopfinger, E. J. & Saramito, P. 2005 Numerical simulations of high density ratio lock-exchange flows. Phys. Fluids 17 (3), 036601.Google Scholar
Fedele, J. J. 2003 Bedforms and gravity underflows in marine environments. PhD thesis, University of Illinois at Urbana-Champaign.Google Scholar
Field, M. E., Gardner, J. V. & Prior, D. B. 1999 Geometry and significance of stacked gullies on the northern California slope. Mar. Geol. 154, 271286.Google Scholar
Fletcher, C. 1991 Computational Techniques for Fluid Dynamics 2. Springer.Google Scholar
Garcia, M. H. 1994 Depositional turbidity currents laden with poorly sorted sediment. J. Hydraul. Engng 120, 12401263.Google Scholar
Garcia, M. H. & Parker, G. 1993 Experiments on the entrainment of sediment into resuspension by a dense bottom current. J. Geophys. Res. 98, 47934807.Google Scholar
Greene, H. G., Maher, M. & Paull, C. K. 2002 Physiography of the Monterey Bay National Marine Sanctuary and implications about continental margin development. Mar. Geol. 181, 5582.Google Scholar
Gyr, A. & Kinzelbach, W. 2004 Bed forms in turbulent channel flow. Appl. Mech. Rev. 57 (1), 7793.Google Scholar
Ham, J. M. & Homsy, G. M. 1988 Hindered settling and hydrodynamic dispersion in quiescent sedimenting suspensions. Intl J. Multiphase Flow 14 (5), 533546.Google Scholar
Hanratty, T. J. 1981 Stability of surfaces that are dissolving or being formed by convective diffusion. Annu. Rev. Fluid Mech. 13, 231252.Google Scholar
Härtel, C., Carlsson, F. & Thunblom, M. 2000 Analysis and direct numerical simulation of the flow at a gravity-current head. Part 2. The lobe-and-cleft instability. J. Fluid Mech. 418, 213229.Google Scholar
Härtel, C., Meiburg, E. & Necker, F. 2000 Analysis and direct numerical simulations of the flow at a gravity current head. Part 1. Flow topology and front speed for slip and no-slip boundaries. J. Fluid Mech. 418, 189212.Google Scholar
Imran, J., Parker, G. & Katopodes, N. 1998 A numerical model of channel inception on submarine fans. J. Geophys. Res. 103, 12191238.CrossRefGoogle Scholar
Izumi, N. 2004 The formation of submarine gullies by turbidity currents. J. Geophys. Res. 109, C03048.Google Scholar
Izumi, N. & Fujii, K. 2006 Channelization on plateaus composed of weakly cohesive fine sediment. J. Geophys. Res. 111, F01012, doi:10.1029/2005JF000345.Google Scholar
Izumi, N. & Parker, G. 1995 Inception of channelization and drainage basin formation: upstream-driven theory. J. Fluid Mech. 283, 341363.Google Scholar
Izumi, N. & Parker, G. 2000 Linear stability analysis of channel inception: downstream-driven theory. J. Fluid Mech. 419, 239262.Google Scholar
Kneller, B. C. & Buckee, C. M. 2000 The structure and fluid mechanics of turbidity currents; a review of some recent studies and their geological implications. Sedimentology 47 (Suppl. 1), 6294.Google Scholar
Komar, P. D. 1969 The channelized flow of turbidity currents with application to Monterey deep-sea fan channel. J. Geophys. Res. 74 (18), 45444558.Google Scholar
Lowe, R. J., Rottman, J. W. & Linden, P. F. 2005 The non-Boussinesq lock-exchange problem. Part 1. Theory and experiments. J. Fluid Mech. 537, 101124.Google Scholar
McAdoo, B. G., Pratson, L. & Orange, D. L. 2000 Submarine landslide geomorphology, US continental slope. Mar. Geol. 169, 103136.Google Scholar
McCaffrey, W. D., Choux, C. M., Baas, J. H. & Haughton, P. D. W. 2003 Spatio-temporal evolution of velocity structure, concentration and grain-size stratification within experimental particulate gravity currents. Mar. Petrol. Geol. 20, 851860.CrossRefGoogle Scholar
Necker, F., Härtel, C., Kleiser, L. & Meiburg, E. 2002 High-resolution simulations of particle-driven gravity currents. Intl J. Multiphase Flow 28, 279300.CrossRefGoogle Scholar
Necker, F., Härtel, C., Kleiser, L. & Meiburg, E. 2005 Mixing and dissipation in particle-driven gravity currents. J. Fluid Mech. 545, 339372.Google Scholar
Normark, W. R. 1989 Observed parameters for turbidity-current flow in channels, Reserve Fan, Lake Superior. J. Sedim. Petrol. 59, 423431.Google Scholar
Parker, G. 1978 Self-formed straight rivers with equilibrium banks and mobile bed Part 1. The sand-silt river. J. Fluid Mech. 89 (1), 109125.CrossRefGoogle Scholar
Parker, G., Garcia, M., Fukushima, M. & Yu, W. 1987 Experiments on turbidity currents over an erodible bed. J. Hydraul. Res. 25, 123147.Google Scholar
Piper, D. J. W. & Savoye, B. 1993 Processes of late quaternary turbidity current flow and deposition on the Var deep-sea fan, north-west Mediterranean sea. Sedimentology 40, 557582.Google Scholar
Raju, N. & Meiburg, E. 1995 The accumulation and dispersion of heavy particles in forced two-dimensional mixing layers. II. The effect of gravity. Phys. Fluids 7 (6), 1241–64.Google Scholar
Revelli, R. & Ridolfi, L. 2000 Inception of channelization over a non-flat bed. Meccanica 35, 457461.Google Scholar
Simpson, J. E. 1997 Gravity Currents in the Environment and the Laboratory, 2nd edn.Cambridge University Press.Google Scholar
Smith, T. R. & Bretherton, F. P. 1972 Stability and the conservation of mass in drainage basin evolution. Water Resour. Res. 8, 15061529.Google Scholar
Stacey, M. W. & Bowen, A. J. 1988 The vertical structure of density and turbidity currents: theory and observations. J. Geophys. Res. 93, 35283542.Google Scholar
Syvitski, J., Field, M., Alexander, C., Orange, D., Gardner, J. & Lun, L. 1996 Continental-slope sedimentation: the view from northern California. Oceanography 9, 163167.CrossRefGoogle Scholar
Thorsness, C. B. & Hanratty, T. J. 1979 Stability of dissolving or depositing surfaces. AIChE J. 25 (4), 697701.CrossRefGoogle Scholar
Wang, Z. & Cheng, N. 2005 Secondary flows over artificial bed strips. Adv. Water Res. 28, 441450.Google Scholar
Zeng, J., Lowe, D. R., Prior, D. B. & Wiseman, W. D. Jr 1991 Flow properties of turbidity currents in Bute Inlet, British Columbia. Sedimentology 38, 975996.CrossRefGoogle Scholar