A simple formula for vertical eddy diffusion coefficients under conditions of nonneutral stability

Abstract

Vertical turbulent transport of heat and momentum in water bodies is often parameterized as the neutral value of the appropriate (vertical) eddy diffusion coefficient, multiplied by a function of the gradient Richardson number. An analysis of previously published formulae for these stability functions shows that they are not consistent with observed values for the ratio between nonneutral and neutral values of the vertical eddy diffusion coefficients [Ueda et al., 1981] nor with observed values of the turbulent Prandtl number or the flux Richardson number [Linden, 1979]. A new formulation for the stability function in the case of turbulent heat transfer is proposed which is of an inverse quadratic form. It is shown that this representation, together with an appropriate inverse linear form in the case of momentum transfer, is in excellent agreement with recent data.