Boundary mixing in a stratified fluid

Abstract

A vertically oscillating grid is used to simulate boundary mixing in the laboratory. The oscillation of the grid creates a turbulent mixing region in its vicinity, and mixing within this region creates a step-like structure in an initial density distribution which varies linearly with depth. If the initial density varies only at the boundary between two homogeneous layers, the same grid turbulence generates additional steps above and below the initial one. The steps, in turn, drive multiple intrusions of mixed fluid away from the boundary and into the non-turbulent interior of the fluid. A compensat- ing return flow carries fluid from the interior into the turbulent mixing region. From the data, the inference is made that the intrusions make a negligible direct contribution to the vertical mass transport. An analytical model of the intrusions, which employs only molecular values of the transport coefficients and also demonstrates negligible vertical mass transport, is consissent with the laboratory observations.Nevertheless, the data indicate that the fluid eventually reaches a homogeneous density by means of the gradual change of the gradient at a rate which is essentially the same both near the grid and far from it. For an initially uniform density profile this change occurs at all heights simultaneously, and for an initial density step it occurs preferentially near the step. Thus in both cases the interior flow must include slow vertical advection away from the horizontal centre plane. These advective currents can be made part of a consistent dynamic model, the buoyant equivalent of the spin- down in a rotating flow, provided that the net effect of the grid mixing includes a decrease in the local slope of the density gradient. This mode of adjustment explains satisfactorily the experimentally observed negligible horizontal density gradients. For the cme of an initially uniform density stratification, the shape of the evolving density gradient is not accounted for. In particular, it is not clear why the gradient changes at mid-depth almost simultaneously with variations at top and bottom boundaries.The vertical mass flux is found to be independent of container length, and it increases with grid frequency of oscillation, amplitude of oscillation and with the mean density gradient.