Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-28T05:23:19.390Z Has data issue: false hasContentIssue false
  • English
  • Français

Turbidity currents interacting with three-dimensional seafloor topography

Published online by Cambridge University Press:  21 March 2014

M. M. Nasr-Azadani  and
E. Meiburg
M. M. Nasr-Azadani
Affiliation:
Department of Mechanical Engineering, University of California at Santa Barbara, Santa Barbara, CA 93106, USA
E. Meiburg*
Affiliation:
Department of Mechanical Engineering, University of California at Santa Barbara, Santa Barbara, CA 93106, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Direct numerical simulations are employed to investigate the interactions of bidisperse turbidity currents with three-dimensional seafloor topography in the form of Gaussian bumps. Results for two different bump heights are compared against currents propagating over a flat surface. The bump heights are chosen such that the current largely flows over the smaller bump, while it primarily flows around the taller bump. Furthermore, the effects of the settling velocity are investigated by comparing turbidity currents with corresponding compositional gravity currents. The influence of the bottom topography on the front velocity of turbidity currents is seen to be much weaker than the influence of the particle settling velocity. Consistent with earlier work on gravity currents propagating over flat boundaries, the influence of the Reynolds number on the front velocity of currents interacting with three-dimensional bottom topography is found to be small, as long as $\mathit{Re}\geq O(1000)$. The lobe-and-cleft structures, on the other hand, exhibit a stronger influence of the Reynolds number. The current/bump interaction deforms the bottom boundary-layer vorticity into traditional horseshoe vortices, with a downwash region in the centre of the wake. At the same time, the vorticity originating in the mixing layer between the current and the ambient interacts with the bump in such a way as to form ‘inverted horseshoe vortices’, with an upwash region in the wake centre. Additional streamwise vortical structures form as a result of baroclinic vorticity generation. The dependence of the sedimentation rate and streamwise vorticity generation on the height of the bump are discussed, and detailed analyses are presented of the energy budget and bottom wall-shear stress. It is shown that for typical laboratory-scale experiments, the range of parameters explored in the present investigation will not give rise to bedload transport or sediment resuspension. Based on balance arguments for the kinetic and potential energy components, a scaling law is obtained for the maximum bump height over which gravity currents can travel. This scaling law is validated by simulation results, and it provides a criterion for distinguishing between ‘short’ and ‘tall’ topographical features. For turbidity currents, this scaling result represents an upper limit. An interesting non-monotonic influence of the bump height is observed on the long-term propagation velocity of the current. On the one hand, the lateral deflection of the current by the bump leads to an effective increase in the current height and its front velocity in the region away from the bump. At the same time, taller bumps result in a more vigorous three-dimensional evolution of the current, accompanied by increased levels of dissipation, which slows the current down. For small bumps, the former mechanism dominates, so that on average the current front propagates faster than its flat bottom counterpart. For currents interacting with larger bumps, however, the increased dissipation becomes dominant, so that they exhibit a reduced front velocity as compared to currents propagating over flat surfaces.

JFM classification

Geophysical and Geological Flows: Gravity currents Geophysical and Geological Flows: Stratified flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 745 , 25 April 2014 , pp. 409 - 443
Copyright
© 2014 Cambridge University Press 

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

Al Ja Aidi, O. S.2000 The influence of topography and flow efficiency on the deposition of turbidites. PhD thesis, University of Leeds.Google Scholar
Armi, L. 1986 The hydraulics of two flowing layers with different densities. J. Fluid Mech. 163 (1), 27–58.Google Scholar
Baker, C. J.1978 Vortex flow around the bases of obstacles. PhD thesis, University of Cambridge.Google Scholar
Baker, C. J. 1979 The laminar horseshoe vortex. J. Fluid Mech. 95 (02), 347–367.Google Scholar
Baker, C. J. 1980 The turbulent horseshoe vortex. J. Wind Engng Ind. Aerodyn. 6 (1), 9–23.Google Scholar
Belcher, S. E. & Hunt, J. C. R. 1998 Turbulent flow over hills and waves. Annu. Rev. Fluid Mech. 30 (1), 507–538.Google Scholar
Benjamin, T. B. 1968 Gravity currents and related phenomena. J. Fluid Mech. 31 (2), 209–248.Google 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, 125–144.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. 110 (C12), C120–C122.Google Scholar
Bonnecaze, R. T., Huppert, H. E. & Lister, J. R. 1993 Particle-driven gravity currents. J. Fluid Mech. 250, 339–369.Google Scholar
Borden, Z. & Meiburg, E. 2013 Circulation based models for Boussinesq gravity currents. Phys. Fluids 25 (10), 101301.Google Scholar
Cantero, M. I., Balachandar, S., Cantelli, A., Pirmez, C. & Parker, G. 2009 Turbidity current with a roof: direct numerical simulation of self-stratified turbulent channel flow driven by suspended sediment. J. Geophys. Res. 114 (C3), C03008.Google Scholar
Cantero, M. I., Lee, J. R., Balachandar, S. & Garcia, M. H. 2007 On the front velocity of gravity currents. J. Fluid Mech. 586, 1–39.Google Scholar
Castro, I. P. & Snyder, W. H. 1993 Experiments on wave breaking in stratified flow over obstacles. J. Fluid Mech. 255, 195–211.Google Scholar
Castro, I. P., Snyder, W. H. & Marsh, G. L. 1983 Stratified flow over three-dimensional ridges. J. Fluid Mech. 135, 261–282.CrossRefGoogle Scholar
Chorin, A. J. 1968 Numerical solution of the Navier–Stokes equations. Maths Comput. 22 (104), 745–762.Google Scholar
Dade, W. & Huppert, H. E. 1995 A box model for non-entraining, suspension-driven gravity surges on horizontal surfaces. Sedimentology 42 (3), 453–470.Google Scholar
de Rooij, F. & Dalziel, S. B. 2001 Time- and space-resolved measurements of the deposition under turbidity currents. Special Publ. Int. Assoc. Sedimentol. 31, 207–215.Google Scholar
Dietrich, W. E. 1982 Settling velocity of natural particles. Water Resour. Res. 18 (6), 1615–1626.CrossRefGoogle Scholar
Doligalski, T. L., Smith, C. R. & Walker, J. D. A. 1994 Vortex interactions with walls. Annu. Rev. Fluid Mech. 26 (1), 573–616.Google Scholar
Eiff, O. S. & Bonneton, P. 2000 Lee-wave breaking over obstacles in stratified flow. Phys. Fluids 12, 1073.Google Scholar
Ellison, T. H. & Turner, J. S. 1959 Turbulent entrainment in stratified flows. J. Fluid Mech. 6 (3), 423–448.Google Scholar
Espath, L. F. R., Pinto, L. C., Laizet, S. & Silvestrini, J. H. 2014 Two-and three-dimensional direct numerical simulation of particle-laden gravity currents. Comput. Geosci. 63, 9–16.CrossRefGoogle Scholar
Garcia, M. & Parker, G. 1993 Experiments on the entrainment of sediment into suspension by a dense bottom current. J. Geophys. Res. 98 (3), 4793–4807.Google Scholar
Gladstone, C., Phillips, J. C. & Sparks, R. S. J. 1998 Experiments on bidisperse, constant-volume gravity currents: propagation and sediment deposition. Sedimentology 45 (5), 833–843.Google Scholar
Gonzalez-Juez, E., Meiburg, E. & Constantinescu, G. 2009 Gravity currents impinging on bottom-mounted square cylinders: flow fields and associated forces. J. Fluid Mech. 631, 65.Google Scholar
Gonzalez-Juez, E., Meiburg, E., Tokyay, T. & Constantinescu, G. 2010 Gravity current flow past a circular cylinder: forces, wall shear stresses and implications for scour. J. Fluid Mech. 649, 69–102.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.Google Scholar
Hallworth, M., Hogg, A. & Huppert, H. E. 1998 Effects of external flow on compositional and particle gravity currents. J. Fluid Mech. 359, 109–142.Google Scholar
Harris, T. C., Hogg, A. J. & Huppert, H. E. 2002 Polydisperse particle-driven gravity currents. J. Fluid Mech. 472 (1), 333–371.Google Scholar
Härtel, C., Carlsson, F. & Thunblom, M. 2000a Analysis and direct numerical simulation of the flow at a gravity-current head. Part 2. The lobe-and-cleft instability. J. Fluid Mech. 418, 213–229.CrossRefGoogle Scholar
Härtel, C., Meiburg, E. & Necker, F. 2000b Analysis and direct numerical simulation 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, 189–212.Google Scholar
Harten, A. 1997 High resolution schemes for hyperbolic conservation laws. J. Comput. Phys. 135 (2), 260–278.Google Scholar
Harten, A., Engquist, B., Osher, S. & Chakravarthy, S. R. 1987 Uniformly high order accurate essentially non-oscillatory schemes, III. J. Comput. Phys. 71 (2), 231–303.CrossRefGoogle Scholar
Huang, H., Imran, J. & Pirmez, C. 2008 Numerical study of turbidity currents with sudden-release and sustained-inflow mechanisms. J. Hydraul. Engng 134 (9), 1199–1209.Google Scholar
Hunt, J. C. R. & Snyder, W. H. 1980 Experiments on stably and neutrally stratified flow over a model three-dimensional hill. J. Fluid Mech. 96 (04), 671–704.Google Scholar
Hunt, J. C. R., Wray, A. A. & Moin, P.1988 Eddies, stream, and convergence zones in turbulent flows. Tech. Rep. CTR-S88. Centre for Turbulence Research.Google Scholar
Huppert, H. E. 1986 The intrusion of fluid mechanics into geology. J. Fluid Mech. 173 (1), 557–594.CrossRefGoogle Scholar
Huppert, H. E. & Simpson, J. E. 1980 The slumping of gravity currents. J. Fluid Mech. 99 (04), 785–799.CrossRefGoogle Scholar
Janocko, M., Cartigny, M. B. J., Nemec, W. & Hansen, E. W. M. 2012 Turbidity current hydraulics and sediment deposition in erodible sinuous channels: laboratory experiments and numerical simulations. Mar. Petrol. Geol.Google Scholar
Kane, I. A., McCaffrey, W. D., Peakall, J. & Kneller, B. C. 2010 Submarine channel levee shape and sediment waves from physical experiments. Sedim. Geol. 223 (1), 75–85.Google Scholar
Kassem, A. & Imran, J. 2004 Three-dimensional modelling of density current. II. Flow in sinuous confined and uncontined channels. J. Hydraul. Res. 42 (6), 591–602.Google Scholar
Kim, J. & Moin, P. 1985 Application of a fractional-step method to incompressible Navier–Stokes equations. J. Comput. Phys. 59 (2), 308–323.Google Scholar
Kneller, B. & McCaffrey, W. D. 1999 Depositional effects of flow non-uniformity and stratification within turbidity currents approaching a bounding slope; deflection, reflection, and facies variation. J. Sedim. Res. 69 (5), 980–991.Google Scholar
Kubo, Y. 2004 Experimental and numerical study of topographic effects on deposition from two-dimensional, particle-driven density currents. Sedim. Geol. 164 (3–4), 311–326.Google Scholar
Kubo, Y. & Nakajima, T. 2002 Laboratory experiments and numerical simulation of sediment-wave formation by turbidity currents. Mar. Geol. 192 (1), 105–121.Google Scholar
Kuenen, P. H. & Migliorini, C. I. 1950 Turbidity currents as a cause of graded bedding. J. Geol. 58, 91–127.Google Scholar
Lesshafft, L., Hall, B., Meiburg, E. & Kneller, B. 2011 Deep-water sediment wave formation: linear stability analysis of coupled flow/bed interaction. J. Fluid Mech. 680 (1), 435–458.Google Scholar
Lin, Q., Lindberg, W. R., Boyer, D. L. & Fernando, H. J. S. 1992 Stratified flow past a sphere. J. Fluid Mech. 240 (1), 315–354.CrossRefGoogle Scholar
Luthi, S. 1981 Experiments on non-channelized turbidity currents and their deposits. Mar. Geol. 40 (3–4), 59–68.Google Scholar
Mason, P. J. & Morton, B. R. 1987 Trailing vortices in the wakes of surface-mounted obstacles. J. Fluid Mech. 175 (1), 247–293.Google Scholar
Mason, P. J. & Sykes, R. I. 1979 Three-dimensional numerical integrations of the Navier–Stokes equations for flow over surface-mounted obstacles. J. Fluid Mech. 91, 433–450.Google Scholar
Meiburg, E. & Kneller, B. 2010 Turbidity currents and their deposits. Annu. Rev. Fluid Mech. 42 (1), 135–156.Google Scholar
Middleton, G. V. 1993 Sediment deposition from turbidity currents. Annu. Rev. Earth Planet. Sci. 21 (1), 89–114.Google Scholar
Migeon, S., Savoye, B., Zanella, E., Mulder, T., Faugères, 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 (2), 179–208.Google Scholar
Mittal, R., Dong, H., Bozkurttas, M., Najjar, F. M., Vargas, A. & von Loebbecke, A. 2008 A versatile sharp interface immersed boundary method for incompressible flows with complex boundaries. J. Comput. Phys. 227 (10), 4825–4852.Google Scholar
Mohd-Yusof, J. 1997 Combined immersed-boundary/B-spline methods for simulations of flow in complex geometries. In CTR Annual Research Briefs pp. 317–327. NASA Ames/Stanford University, (1).Google 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 (2), 435–463.Google Scholar
Nasr-Azadani, M. M., Hall, B. & Meiburg, E. 2013 Polydisperse turbidity currents propagating over complex topography: comparison of experimental and depth-resolved simulation results. Comput. Geosci. 53 (0), 141–153.Google Scholar
Nasr-Azadani, M. M. & Meiburg, E. 2011 TURBINS: an immersed boundary, Navier–Stokes code for the simulation of gravity and turbidity currents interacting with complex topographies. Comput. Fluids 45 (1), 14–28.Google Scholar
Nasr-Azadani, M. M. & Meiburg, E. 2013 Influence of seafloor topography on the depositional behaviour of bi-disperse turbidity currents: a three-dimensional, depth-resolved numerical investigation. Environ. Fluid Mech. doi: 10.1007/s10652–013-9292-5.Google Scholar
Necker, F., Härtel, C., Kleiser, L. & Meiburg, E. 2002 High-resolution simulations of particle-driven gravity currents. Intl J. Multiphase Flow 28 (2), 279–300.Google Scholar
Necker, F., Härtel, C., Kleiser, L. & Meiburg, E. 2005 Mixing and dissipation in particle-driven gravity currents. J. Fluid Mech. 545, 339–372.Google 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 (1), 23–58.CrossRefGoogle Scholar
Normark, W. R., Posamentier, H. & Mutti, E. 1993 Turbidite systems: state of the art and future directions. Rev. Geophys. 31 (2), 91–116.Google Scholar
Oehy, C. D. & Schleiss, A. J. 2007 Control of turbidity currents in reservoirs by solid and permeable obstacles. J. Hydraul. Engng 133 (6), 637–648.Google Scholar
Ooi, S. K., Constantinescu, G. & Weber, L. 2009 Numerical simulations of lock-exchange compositional gravity current. J. Fluid Mech. 635, 361.Google Scholar
Peakall, J., Amos, K. J., Keevil, G. M., William Bradbury, P. & Gupta, S. 2007 Flow processes and sedimentation in submarine channel bends. Mar. Petrol. Geol. 24 (6), 470–486.Google Scholar
Pirmez, C. & Imran, J. 2003 Reconstruction of turbidity currents in Amazon channel. Mar. Petrol. Geol. 20 (6), 823–849.Google Scholar
Rottman, J. W. & Simpson, J. E. 1983 Gravity currents produced by instantaneous releases of a heavy fluid in a rectangular channel. J. Fluid Mech. 135 (1), 95–110.Google Scholar
Sau, A., Hwang, R. R., Sheu, T. W. H. & Yang, W. C. 2003 Interaction of trailing vortices in the wake of a wall-mounted rectangular cylinder. Phys. Rev. E 68 (5), 056303.Google Scholar
Sequeiros, O. E., Spinewine, B., Beaubouef, R. T., Sun, T., García, M. H. & Parker, G. 2010 Characteristics of velocity and excess density profiles of saline underflows and turbidity currents flowing over a mobile bed. J. Hydraul. Engng 136 (7), 412–433.Google Scholar
Shin, J. O., Dalziel, S. B. & Linden, P. F. 2004 Gravity currents produced by lock exchange. J. Fluid Mech. 521, 1–34.Google Scholar
Simpson, J. E. 1972 Effects of the lower boundary on the head of a gravity current. J. Fluid Mech. 53 (04), 759–768.Google Scholar
Simpson, J. E. 1997 Gravity Currents: In the Environment and the Laboratory. 2nd edn.. Cambridge University Press.Google Scholar
Simpson, J. E. & Britter, R. E. 1979 The dynamics of the head of a gravity current advancing over a horizontal surface. J. Fluid Mech. 94 (3), 477–495.Google Scholar
Smolarkiewicz, P. K. & Rotunno, R. 1989 Low froude number flow past three-dimensional obstacles. Part I: baroclinically generated lee vortices. J. Atmos. Sci. 46 (8), 1154–1164.Google Scholar
Smolarkiewicz, P. K. & Rotunno, R. 1990 Low froude number flow past three-dimensional obstacles. Part II: upwind flow reversal zone. J. Atmos. Sci. 47 (12), 1498–1511.Google Scholar
Snyder, W. H., Britter, R. E. & Hunt, J. C. R. 1979 A fluid modelling study of the flow structure and plume impingement on a three dimensional hill in stably stratified flow. In Wind Engineering-Proceedings of the Fifth International Conference vol. vol. 1, pp. 319–329. Pergamon Press.Google Scholar
Snyder, W. H., Hunt, J. C. R., Lee, J. T., Castro, I. P., Lawson, R. E., Eskridge, R. E., Thompson, R. S. & Ogawa, Y. 1985 Structure of strongly stratified flow over hills: dividing-streamline concept. J. Fluid Mech. 152, 249–288.Google Scholar
Strauss, M. & Glinsky, M. E. 2012 Turbidity current flow over an erodible obstacle and phases of sediment wave generation. J. Geophys. Res. 117 (C6), C06007.Google Scholar
Syvitski, J. P., Alexander, C. R., Field, M. E., Gardner, J. V., Orange, D. L. & Yun, J. W. 1996 Continental-slope sedimentation: the view from northern California. Oceanography 9 (3), 163–167.Google Scholar
Tokyay, T., Constantinescu, G. & Meiburg, E. 2012 Tail structure and bed friction velocity distribution of gravity currents propagating over an array of obstacles. J. Fluid Mech. 1 (1), 1–40.Google Scholar
Tseng, Y. H., Meneveau, C. & Parlange, M. B. 2006 Modelling flow around bluff bodies and predicting urban dispersion using large eddy simulation. Environ. Sci. Technol. 40 (8), 2653–2662.Google Scholar
Vinokur, M. 1983 On one-dimensional stretching functions for finite-difference calculations. J. Comput. Phys. 50 (2), 215–234.Google Scholar
Vosper, S. B., Castro, I. P., Snyder, W. H. & Mobbs, S. D. 1999 Experimental studies of strongly stratified flow past three-dimensional orography. J. Fluid Mech. 390, 223–249.Google Scholar
Winters, K. B. & Armi, L. 2012 Hydraulic control of continuously stratified flow over an obstacle. J. Fluid Mech. 700, 502–513.Google Scholar
Winters, K. B., Lombard, P. N., Riley, J. J. & D’Asaro, E. A. 1995 Available potential energy and mixing in density-stratified fluids. J. Fluid Mech. 289 (1), 115–128.Google Scholar
Woods, A. W., Bursik, M. I. & Kurbatov, A. V. 1998 The interaction of ash flows with ridges. Bull. Volcanol. 60 (1), 38–51.Google Scholar
Wynn, R. B. & Stow, D. A. V. 2002 Classification and characterisation of deep-water sediment waves. Mar. Geol. 192 (1–3), 7–22.Google Scholar
Wynn, R. B., Weaver, P. P. E., Ercilla, G., Stow, D. A. V. & Masson, D. G. 2000 Sedimentary processes in the Selvage sediment-wave field, NE Atlantic: new insights into the formation of sediment waves by turbidity currents. Sedimentology 47 (6), 1181–1197.Google Scholar
Xu, J. P., Noble, M. A. & Rosenfeld, L. K. 2004 In-situ measurements of velocity structure within turbidity currents. Geophys. Res. Lett. 31 (9), L09311.Google Scholar
Yalin, M. S. & Karahan, E. 1979 Inception of sediment transport. J. Hydraul. Div. 105 (11), 1433–1443.Google Scholar