Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-29T22:01:31.676Z Has data issue: false hasContentIssue false
  • English
  • Français

Gravity currents propagating into shear

Published online by Cambridge University Press:  05 August 2015

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

An analytical vorticity-based model is introduced for steady-state inviscid Boussinesq gravity currents in sheared ambients. The model enforces the conservation of mass and horizontal and vertical momentum, and it does not require any empirical closure assumptions. As a function of the given gravity current height, upstream ambient shear and upstream ambient layer thicknesses, the model predicts the current velocity as well as the downstream ambient layer thicknesses and velocities. In particular, it predicts the existence of gravity currents with a thickness greater than half the channel height, which is confirmed by direct numerical simulation (DNS) results and by an analysis of the energy loss in the flow. For high-Reynolds-number gravity currents exhibiting Kelvin–Helmholtz instabilities along the current/ambient interface, the DNS simulations suggest that for a given shear magnitude, the current height adjusts itself such as to allow for maximum energy dissipation.

JFM classification

Geophysical and Geological Flows: Geophysical and Geological Flows Geophysical and Geological Flows: Gravity currents Geophysical and Geological Flows: Stratified flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 778 , 10 September 2015 , pp. 552 - 585
Check for updates
Copyright
© 2015 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

Benjamin, T. B. 1968 Gravity currents and related phenomena. J. Fluid Mech. 31 (2), 209–248.Google Scholar
Borden, Z. & Meiburg, E. 2013a Circulation based models for Boussinesq gravity currents. Phys. Fluids 25 (10), 101301.Google Scholar
Borden, Z. & Meiburg, E. 2013b Circulation-based models for Boussinesq internal bores. J. Fluid Mech. 726, R1.Google Scholar
Bryan, G. H. & Rotunno, R. 2014a Gravity currents in confined channels with environmental shear. J. Atmos. Sci. 71 (3), 1121–1142.Google Scholar
Bryan, G. H. & Rotunno, R. 2014b The optimal state for gravity currents in shear. J. Atmos. Sci. 71 (1), 448–468.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.CrossRefGoogle Scholar
Härtel, C., Meiburg, E. & Necker, F. 2000 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
Hopfinger, E. J. 1983 Snow avalanche motion and related phenomena. Annu. Rev. Fluid Mech. 15 (1), 47–76.Google Scholar
Huerre, P. & Monkewitz, P. A. 1990 Local and global instabilities in spatially developing flows. Annu. Rev. Fluid Mech. 22 (1), 473–537.Google Scholar
von Karman, T. 1940 The engineer grapples with nonlinear problems. Bull. Am. Math. Soc. 46 (8), 615–683.Google Scholar
Klemp, J. B., Rotunno, R. & Skamarock, W. C. 1994 On the dynamics of gravity currents in a channel. J. Fluid Mech. 269, 169–198.Google Scholar
Linden, P. 2012 Gravity currents – theory and laboratory experiments. In Buoyancy-Driven Flows (ed. Chassignet, E., Cenedese, C. & Verron, J.), Cambridge University Press.Google Scholar
Meiburg, E. & Kneller, B. 2010 Turbidity currents and their deposits. Annu. Rev. Fluid Mech. 42 (1), 135–156.CrossRefGoogle Scholar
Moncrieff, M. W. 1978 The dynamical structure of two-dimensional steady convection in constant vertical shear. Q. J. R. Meteorol. Soc. 104 (441), 543–567.Google Scholar
Moncrieff, M. W. 1992 Organized convective systems: archetypal dynamical models, mass and momentum flux theory, and parametrization. Q. J. R. Meteorol. Soc. 118 (507), 819–850.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.CrossRefGoogle 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. 2014 Turbidity currents interacting with three-dimensional seafloor topography. J. Fluid Mech. 745, 409–443.CrossRefGoogle Scholar
Nokes, R. I., Davidson, M. J., Stepien, C. A., Veale, W. B. & Oliver, R. L. 2008 The front condition for intrusive gravity currents. J. Hydraul. Res. 46 (6), 788–801.Google Scholar
Rotunno, R., Klemp, J. B. & Weisman, M. L. 1988 A theory for strong, long-lived squall lines. J. Atmos. Sci. 45 (3), 463–485.Google Scholar
Saffman, P. G. 1992 Vortex Dynamics. Cambridge University Press.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. 1997 Gravity Currents: In the Environment and the Laboratory, 2nd edn. Cambridge University Press.Google Scholar
Ungarish, M. 2010 An Introduction to Gravity Currents and Intrusions. CRC Press.Google Scholar
Weckwerth, T. M. & Wakimoto, R. M. 1992 The initiation and organization of convective cells atop a cold-air outflow boundary. Mon. Weath. Rev. 120 (10), 2169–2187.Google Scholar
Xu, Q. 1992 Density currents in shear flows – a two-fluid model. J. Atmos. Sci. 49 (6), 511–524.Google Scholar
Xu, Q. & Moncrieff, M. W. 1994 Density current circulations in shear flows. J. Atmos. Sci. 51 (3), 434–446.Google Scholar
Xu, Q., Xue, M. & Droegemeer, K. K. 1996 Numerical simulations of density currents in sheared environments within a vertically confined channel. J. Atmos. Sci. 53 (5), 770–786.Google Scholar
Xue, M. 2000 Density currents in two-layer shear flows. Q. J. R. Meteorol. Soc. 126 (565), 1301–1320.Google Scholar
Xue, M. 2002 Density currents in shear flows: effects of rigid lid and cold-pool internal circulation, and application to squall line dynamics. Q. J. R. Meteorol. Soc. 128 (579), 47–73.Google Scholar
Xue, M., Xu, Q. & Droegemeier, K. K. 1997 A theoretical and numerical study of density currents in nonconstant shear flows. J. Atmos. Sci. 54 (15), 1998–2019.2.0.CO;2>CrossRefGoogle Scholar