An experiment on boundary mixing: mean circulation and transport rates

Abstract

An experiment is described in which a turbulent boundary layer was generated along a sloping wall of a laboratory tank containing salt-stratified fluid. Initially, the pycnocline separating the upper fresh-water layer from the lower saline layer was relatively thin; it thickened in response to the mixing as the experiment proceeded. Two types of mean circulation developed as a result of the boundary mixing. In the boundary layer, counterflowing mean streams were observed that augmented the diffusion of salt up- and downslope. This augmented dispersion in turn tended to spread the salt beyond the depth range of the pycnocline in the ambient fluid, producing a mean convergence in the boundary layer and intrusions from the layer into the ambient fluid.The evolving density structure in the ambient fluid was measured by conductivity-probe traverses, from which the net buoyancy flux (or salt flux) and volume flux in the boundary layer were determined. The level of zero volume flux was found to coincide closely with the level of maximum stability frequency N, so that the buoyancy transport across this level was entirely the result of turbulent dispersion in the boundary layer. At other levels, the convective transports up and down contribute significantly. A simple theory provides scaling in terms of the laboratory parameters; in terms of the inferred overall turbulent viscosity νe, the buoyancy transport resulting from boundary-layer dispersion was found to be \[ F_{\rm B} = 0.60 \left\{\frac{\nu_{\rm e}N(z)}{\sin\theta}\right\}^{\frac{3}{2}}\cos^2\theta, \] and the intrusion velocity into the ambient fluid is \[ v_1 = 0.42\frac{\nu_{\rm e}^{\frac{3}{2}}}{N^{\frac{1}{2}}h^2}\frac{\cos^2\theta}{(\sin\theta)^{\frac{3}{2}}}, \] where θ is the angle of the sloping bed. These expressions must become invalid when θ becomes vanishingly small; their application to estuarine and continental slope flows is discussed briefly.

VERTICAL MIXING, ENERGY, AND THE GENERAL CIRCULATION OF THE OCEANS

“…It has been known for a long time that waves focusing into the canyons can produce energy densities far in excess of those found in the open sea, with consequent greatly enhanced dissipation (Petruncio et al 1998, Kunze et al 2002. Dissipative boundary layers in a rotating stratified fluid can be remarkably intricate (Phillips et al 1986, Garrett et al 1993, and the subject is not well explored. These layers, and the near-hyperbolic behavior of inviscid waves, render computation of the flow field a serious challenge to any large-scale numerical model.…”

Wave-Modified Turbidites: Combined-Flow Shoreline and Shelf Deposits, Cambrian, Antarctica

“…This has been demonstrated in the Modern for the cross-shelf movement of fluid mud layers (Traykovski et al 2000;Wright et al 2001). Experimental studies have attempted to model wave-modified turbidity currents but have generally been constructed with geologically unrealistic conditions (Thomas and Simpson 1985;Linden and Simpson 1986;Phillips et al 1986;Simpson 1987;Noh and Fernando 1992). It is clear, however, that turbulence added by waves must be strong enough to enhance bottom-boundary-layer turbidity but not so high as to cause excessive diffusion of the gravity-driven dispersion into the overlying water column.…”

Tidal Mixing Events on the Deep Flanks of Kaena Ridge, Hawaii

“…When turbulent mixing in a stratified layer occurs along a sloping boundary, mixed fluid is exported from the boundary layer to the interior, and undisturbed stratified fluid is incorporated into the boundary layer (Phillips et al 1986;Garrett 1991). The mixed water, but not the turbulence itself, can then spread laterally (e.g., via stirring by mesoscale variability) along neutral surfaces into the ocean's interior (Munk and Wunsch 1998).…”