Rapid gravitational adjustment of horizontal shear flows

• Published in: Journal of fluid mechanics Vol. 721; pp. 86 - 117
• Main Authors: White, Brian L., Helfrich, Karl R.
• Format: Journal Article
• Language: English
• Published: Cambridge, UK Cambridge University Press 25.04.2013
• Subjects: Computational fluid dynamics; Dynamics of the ocean (upper and deep oceans); Earth, ocean, space; Exact sciences and technology; External geophysics; Flow control; Fluid flow; Gravitation; Gravity; Horizontal; Oceans; Physics of the oceans; Shear strength; Three dimensional; Turbulence; Turbulent flow; Vortices; shear layers; stratified flows; gravity currents; Gravity current; digital simulation; Ocean dynamics; Shear layer; Modeling; Density stratification; Stratified flow
• ISSN: 0022-1120; 1469-7645
• DOI: 10.1017/jfm.2013.41

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.