Skip to main content Accessibility help
×
Home

Rapid gravitational adjustment of horizontal shear flows

  • Brian L. White (a1) and Karl R. Helfrich (a2)

Abstract

The evolution of a horizontal shear layer in the presence of a horizontal density gradient is explored by three-dimensional numerical simulations. These flows exhibit characteristics of both free shear flows and gravity currents, but have complex dynamics due to strong interactions between the turbulent features of each. Vertical vortices produced by horizontal shear are tilted and stretched by the gravitational adjustment, rapidly enhancing vorticity. Shear intensification at frontal convergences produces high-wavenumber vertical vorticity and the slumping of the density interface produces horizontal Kelvin–Helmholtz vortices typical of a gravity current. The interaction between these instabilities promotes a rapid transition to three-dimensional turbulence. The flow development depends on the relative time scales of shear instability and gravitational adjustment, described by a parameter $\gamma $ (where the limits $\gamma \rightarrow \infty $ and $\gamma \rightarrow 0$ represent a pure gravity current and a pure mixing layer, respectively). The growth rate of three-dimensional instability and the mixing increase for smaller $\gamma $ . When $\gamma $ is sufficiently small, there are two distinct regimes: an early period of during which the interface grows rapidly, followed by horizontal diffusive growth. Numerical results are consistent with field observations of tidal separation flows in the Haro Strait (Farmer, Pawlowicz & Jiang, Dyn. Atmos. Oceans., vol. 36, 2002, pp. 43–58), including the magnitude of downwelling vertical currents, horizontal scales of surface vortex features and mixing rate.

Copyright

Corresponding author

Email address for correspondence: bwhite@unc.edu

References

Hide All
Almgren, A., Bell, J., Colella, P., Howell, L. & Welcome, M. 1998 A conservative adaptive projection method for the variable density incompressible Navier–Stokes equations. J. Comput. Phys. 142, 146.
Aspden, A., Nikiforakis, N., Dalziel, S. & Bell, J. B. 2008 Analysis of implicit les methods. Comm. App. Math. Com. Sc. 3 (1), 103126.
Basak, S. & Sarkar, S. 2006 Dynamics of a stratified shear layer with horizontal shear. J. Fluid Mech. 568, 1954.
Benjamin, T. 1968 Gravity currents and related phenomena. J. Fluid Mech. 31, 209248.
Boccaletti, G., Ferrari, R. & Fox-Kemper, B. 2007 Mixed layer instabilities and restratification. J. Phys. Oceanogr. 37 (9), 22282250.
Boulanger, N., Meunier, P. & Dizès, S. L. 2008 Tilt-induced instability of a stratified vortex. J. Fluid Mech. 596, 120.
Brown, G. & Roshko, A. 1974 On density effects and large structure in turbulent mixing layers. J. Fluid Mech. 64, 775816.
Carpenter, J. R., Balmforth, N. J. & Lawrence, G. A. 2010 Identifying unstable modes in stratified shear layers. Phys. Fluids 22 (5), 054104.
Corcos, G. & Lin, S. 1984 The mixing layer - deterministic models of a turbulent-flow 2. The origin of the 3-dimensional motion. J. Fluid Mech. 139 (FEB), 6795.
Farmer, D., Pawlowicz, R. & Jiang, R. 2002 Tilting separation flows: a mechanism for intense vertical mixing in the coastal ocean. Dyn. Atmos. Oceans. 36 (1–3), 4358.
Hartel, 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, 213229.
Hartel, 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, 189212.
Huerre, P. 1983 Finite amplitude evolution of mixing layers in the presence of solid boundaries. J. de Méc. Théor. Appl. 121145.
Ivey, G. N., Winters, K. B. & Koseff, J. R. 2008 Density stratification, turbulence, but how much mixing?. Annu. Rev. Fluid Mech. 40, 169184.
Lasheras, J. & Choi, H. 1988 3-dimensional instability of a plane free shear-layer - an experimental-study of the formation and evolution of streamwise vortices. J. Fluid Mech. 189, 53&.
Lawrie, A. & Dalziel, S. 2011a Turbulent diffusion in tall tubes. I. Models for Rayleigh–Taylor instability. Phys. Fluids 23, 085109, doi:10.1063/1.3614477.
Lawrie, A. & Dalziel, S. 2011b Turbulent diffusion in tall tubes. II. Confinement by stratification. Phys. Fluids 23, 085109 DOI: 10.1063/1.3622770.
Linden, P. & Simpson, J. 1986 Gravity-driven flows in a turbulent fluid. J. Fluid Mech. 172, 481497.
Margolin, L. G., Smolarkiewicz, P. K. & Wyszogradzki, A. A. 2006 Dissipation in implicit turbulence models: a computational study. J. Appl. Mech. 73 (3), 469473.
Michalke, A. 1964 On the inviscid instability of the hyperbolic tangent velocity profile. J. Fluid Mech. 19 (4), 543556.
Moin, P. & Mahesh, K. 1998 Direct numerical simulation: a tool in turbulence research. Annu. Rev. Fluid Mech. 30, 539578.
Monismith, S., Kimmerer, W., Burau, J. & Stacey, M. 2002 Structure and flow-induced variability of the subtidal salinity field in northern San Francisco Bay. J. Phys. Oceanography 32 (11), 30033019.
Peltier, W. & Caulfield, C. 2003 Mixing efficiency in stratified shear flows. Annu. Rev. Fluid Mech. 35, 135167.
Pierrehumbert, R. & Widnall, S. 1982 The two- and three-dimensional instabilities of a spatially periodic shear layer. J. Fluid Mech. 114, 5982.
Piotrowski, Z., Smolarkiewicz, P., Malinowski, S. & Wyszogrodzki, A. 2009 On numerical realizability of thermal convection. J. Comput. Phys. 228, 62686290.
Shih, L., Koseff, J., Ivey, G. & Ferziger, J. 2005 Parameterization of turbulent fluxes and scales using homogeneous sheared stably stratified turbulence simulations. J. Fluid Mech. 525, 193214.
Simpson, J. E. 1999 Gravity Currents: In the Environment and the Laboratory, 2nd edn. Cambridge University Press.
Waite, M. & Smolarkiewicz, P. 2008 Instability and breakdown of a vertical vortex pair in a strongly stratified fluid. J. Fluid Mech. 606, 239273.
Winant, C. & Browand, F. 1974 Vortex pairing, the mechanism of turbulent mixing-layer growth at moderate Reynolds number. J. Fluid Mech. 63, 237255.
Winters, K., Lombard, P., Riley, J. & D’Asaro, E. 1995 Available potential energy and mixing in density-stratified fluids. J. Fluid Mech..
Young, W. 1994 The subinertial mixed-layer approximation. J. Phys. Oceanogr. 24 (8), 18121826.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

JFM classification

Related content

Powered by UNSILO

Rapid gravitational adjustment of horizontal shear flows

  • Brian L. White (a1) and Karl R. Helfrich (a2)

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.