Setting the length Scale in a Second-Order Closure Model Of the Unstratified Bottom Boundary Layer

Abstract

Frequently the mixing length l in second-order closure models is assumed to have a constant value l0 = ?L at large distances from the bottom with a magnitude proportional to the first moment L of turbulent intensity. Although it is often stated that turbulence closure model results are relatively insensitive to the value of mixing length parameter ?, we show that this is not the case for a second-order Level II model of the steady bottom boundary layer in an unstratified fluid. In particular, the eddy viscosity and diffusivity depend strongly on ?. Available oceanic data on geostrophic drag ratio lead to a value of ? of approximately 0.2?0.3. Atmospheric data for steady flow suggest a smaller value of 0.05?0.1 although the atmospheric observations are ambiguous about the choice of ?, possibly because it is difficult to find truly neutrally stratified and steady-state conditions in the bottom boundary layer. A value of ? between 0.18 and 0.20 is required for the model to match a similarity theory having a linear?exponential form for viscosity. Fitting an M2 tidal current profile at a station in Admiralty Inlet, Washington, with an oscillatory analog of the model yields ? = 0.20 ± 0.04.