Toward a turbulence constitutive relation for geophysical flows
This article addresses and resolves the possibility of a constitutive relation for single-point second-order closures for classes of rotating and stratified flows relevant to geophysics. Physical situations in which a geostrophic balance is attained are described. We discuss also closely related issues of frame-indifference, horizontal divergence, and the Taylor-Proudman theorem. It is shown that, in the absence of vortex stretching along the axis of rotation, turbulence is frame-indifferent. Unfortunately, no turbulence closures are consistent with this frame-indifference that is frequently an important feature of rotating or quasi-geostrophic flows. Thus we derive and discuss a geostrophic constraint which ensures that the modeled second-moment equations are frame-invariant, in the appropriate limit. It is shown that rotating, stratified, and shallow water flows are situations in which such a constitutive relation procedure can be useful.
scientific article; zbMATH DE number 1174714