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Deep-water sediment wave formation: linear stability analysis of coupled flow/bed interaction

Published online by Cambridge University Press:  18 May 2011

L. LESSHAFFT ,
B. HALL ,
E. MEIBURG  and
B. KNELLER
L. LESSHAFFT
Affiliation:
Laboratoire d'Hydrodynamique, CNRS – École Polytechnique, 91128 Palaiseau, France Department of Mechanical Engineering, University of California, Santa Barbara, CA 93106, USA
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
*
†Email address for correspondence: [email protected]
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Abstract

A linear stability analysis is carried out for the interaction of an erodible sediment bed with a sediment-laden, stratified flow above the bed, such as a turbidity or bottom current. The fluid motion is described by the full, two-dimensional Navier–Stokes equations in the Boussinesq approximation, while erosion is modelled as a diffusive flux of particles from the bed into the fluid. The stability analysis shows the existence of both Tollmien–Schlichting and internal wave modes in the stratified boundary layer. For the internal wave mode, the stratified boundary layer acts as a wave duct, whose height can be determined analytically from the Brunt–Väisälä frequency criterion. Consistent with this criterion, distinct unstable perturbation wavenumber regimes exist for the internal wave mode, which are associated with different numbers of pressure extrema in the wall-normal direction. For representative turbidity current parameters, the analysis predicts unstable wavelengths that are consistent with field observations. As a key condition for instability to occur, the base flow velocity boundary layer needs to be thinner than the corresponding concentration boundary layer. For most of the unstable wavenumber ranges, the phase relations between the sediment bed deformation and the associated wall shear stress and concentration perturbations are such that the sediment waves migrate in the upstream direction, which again is consistent with field observations.

JFM classification

Geophysical and Geological Flows: Geophysical and Geological Flows Geophysical and Geological Flows: Internal waves Geophysical and Geological Flows: Sediment transport
Type
Papers
Information
Journal of Fluid Mechanics , Volume 680 , 10 August 2011 , pp. 435 - 458
Copyright
Copyright © Cambridge University Press 2011

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References

REFERENCES

Allen, J. R. L. 1970 Physical Processes of Sedimentation. Unwin University Books.Google 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: Oceans 110 (C12022), doi:10.10129/2005JC002927.CrossRefGoogle Scholar
Canuto, C., Hussaini, M. J., Quarteroni, A. & Zang, T. A. 2006 Spectral Methods, Fundamentals in Single Domains. Springer.CrossRefGoogle Scholar
Colombini, M. 2004 Revisiting the linear theory of sand dune formation. J. Fluid Mech. 502, 1–16.CrossRefGoogle Scholar
Colombini, M. & Stocchino, A. 2008 Finite-amplitude river dunes. J. Fluid Mech. 611, 283–306.CrossRefGoogle Scholar
Engelund, R. & Fredsoe, J. 1982 Sediment ripples and dunes. Annu. Rev. Fluid Mech. 14, 13–37.CrossRefGoogle Scholar
Fildani, A., Normark, W. R., Kostic, S. & Parker, G. 2006 Channel formation by flow-stripping: large-scale scour features along the Monterey East Channel and their relation to sediment waves. Sedimentology 53, 1265–1287.CrossRefGoogle Scholar
Flood, R. D. 1988 A lee wave model for deep-sea mudwave activity. Deep-Sea Res. 35 (6), 973–983.CrossRefGoogle Scholar
Garcia, M. H. & Parker, G. 1993 Experiments on the entrainment of sediment into resuspension by a dense bottom current. J. Geophys. Res. 98, 4793–4807.CrossRefGoogle Scholar
Hall, B., Meiburg, E. & Kneller, B. 2008 Channel formation by turbidity currents: Navier–Stokes-based linear stability analysis. J. Fluid Mech. 615, 185–210.CrossRefGoogle Scholar
Heezen, B. C., Tharp, M. & Ewing, M. 1959 The floors of the oceans. 1. The North Atlantic. GSA Spec. Pap. 65, 122 pp.Google Scholar
Hill, P. S. 1998 Controls on floc size in the sea. Oceanography 11 (2), 13–18.CrossRefGoogle Scholar
Kennedy, J. F. 1969 The formation of sediment ripples, dunes and antidunes. Annu. Rev. Fluid Mech. 1, 147–168.CrossRefGoogle Scholar
Kubo, Y. & Nakajima, T. 2002 Laboratory experiments and numerical simulation of sediment-wave formation by turbidity currents. Mar. Geol. 192, 105–121.CrossRefGoogle Scholar
Lewis, K. B. & Pantin, H. M. 2002 Channel-axis, overbank and drift sediment waves in the southern Hikurangi Trough, New Zealand. Mar. Geol. 192, 123–151.CrossRefGoogle Scholar
Lonsdale, P. F. & Hollister, C. D. 1979 A near-bottom traverse of Rockall Trough: hydrographic and geological inferences. Oceanol. Acta 2, 91–105.Google Scholar
Mack, L. M. 1976 A numerical study of the temporal eigenvalue spectrum of the Blasius boundary layer. J. Fluid Mech. 73, 497–520.CrossRefGoogle Scholar
Meiburg, E. & Kneller, B. 2010 Turbidity currents and their deposits. Annu. Rev. Fluid Mech. 42, 135–156.CrossRefGoogle Scholar
Migeon, S., Savoye, B., Zanella, E., Mulder, T., Faugéres, J.-C. & Weber, O. 2001 Detailed seismic-reflection and sedimentary study of turbidite sediment waves on the Var Sedimentary Ridge (SE France): significance for sediment transport and deposition and for the mechanisms of sediment wave construction. Mar. Petrol. Geol. 18, 179–208.CrossRefGoogle Scholar
Nakajima, T. & Satoh, M. 2001 The formation of large mudwaves by turbidity currents on the levees of the Toyama deep-sea channel, Japan Sea. Sedimentology 48, 435–463.CrossRefGoogle Scholar
Necker, F., Härtel, C., Kleiser, L. & Meiburg, E. 2002 High-resolution simulations of particle-driven gravity currents. Intl J. Multiphase Flow 28, 279–300.CrossRefGoogle Scholar
Necker, F., Härtel, C., Kleiser, L. & Meiburg, E. 2005 Mixing and dissipation in particle-driven gravity currents. J. Fluid Mech. 545, 339–372.CrossRefGoogle Scholar
Normark, W. R., Hess, G. R., Stow, D. A. V. & Bowen, A. J. 1980 Sediment waves on the Monterey fan levee: a preliminary physical interpretation. Mar. Geol. 37, 1–18.CrossRefGoogle Scholar
Normark, W. R., Piper, D. J. W., Posamentier, H., Pirmez, C. & Migeon, S. 2002 Variability in form and growth of sediment waves on turbidite channel levees. Mar. Geol. 192, 23–58.CrossRefGoogle 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), 109–125.CrossRefGoogle Scholar
Peakall, J., McCaffrey, W. D. & Kneller, B. C. 2000 A process model for the evolution, morphology, and architecture of sinuous submarine channels. J. Sedim. Res. 70 (3), 434–448.CrossRefGoogle Scholar
Piper, D. J. W. & Normark, W. R. 1983 Turbidite depositional patterns and flow characteristics, Navy submarine fan, California Borderland. Sedimentology 30, 681–694.CrossRefGoogle Scholar
Queney, P. 1948 The problem of air flow over mountains: a summary of theoretical studies. Bull. Am. Meteorol. Soc. 29, 16–26.CrossRefGoogle Scholar
Raudkivi, A. J. 1966 Bed forms in alluvial channels. J. Fluid Mech. 26 (3), 507–514.CrossRefGoogle Scholar
Reynolds, A. J. 1976 A decades' investigation of the stability of erodible stream beds. Nord. Hydrol. 7, 161–180.CrossRefGoogle Scholar
Savoye, B., Piper, D. J. W. & Droz, L. 1993 Plio-Pleistocene evolution of the Var deep-sea fan off the French Riviera. Mar. Petrol. Geol. 10, 550–571.CrossRefGoogle Scholar
Schmid, P. J. & Henningson, D. S. 2001 Stability and Transition in Shear Flows. Springer.CrossRefGoogle Scholar
Shanmugam, G. 2006 Deep-water Processes and Facies Models: Implications for Sandstone Petroleum Reservoirs, p. 86. Elsevier.Google Scholar
Stacey, M. W. & Bowen, A. J. 1988 The vertical structure of density and turbidity currents: Theory and observations. J. Geophys. Res. 93, 3528–3542.CrossRefGoogle Scholar
Sun, T. & Parker, G. 2005 Transportational cyclic steps created by flow over an erodible bed. Part 2. Theory and numerical simulation. J. Hydraul. Res. 43 (5), 502–514.CrossRefGoogle Scholar
Taki, K. & Parker, G. 2005 Transportational cyclic steps created by flow over an erodible bed. Part 1. Experiments. J. Hydraul. Res. 43 (5), 488–501.CrossRefGoogle Scholar
Turner, J. S. 1973 Buoyancy Effects in Fluids. Cambridge University Press.CrossRefGoogle Scholar
Wynn, R. B., Masson, D. G., Stow, D. A. V. & Weaver, P. P. E. 2000 a Turbidity current sediment waves on the submarine slopes of the western Canary Islands. Mar. Geol. 163, 185–198.CrossRefGoogle Scholar
Wynn, R. B. & Stow, D. A. V. 2002 Classification and characterisation of deep-water sediment waves. Mar. Geol. 192, 7–22.CrossRefGoogle Scholar
Wynn, R. B., Weaver, P. P. E., Ercilla, G., Stow, D. A. V. & Masson, D. G. 2000 b Sedimentary processes in the Selvage sediment-wave field, NE Atlantic: new insights into the formation of sediment waves by turbidity currents. Sedimentology 47, 1181–1197.CrossRefGoogle Scholar