LES Study of Vertical Eddy Diffusivity Estimation in Bottom Boundary Layers

Osborn's method is commonly used to obtain diffusion coefficient K from the turbulent dissipation rate epsilon. This method is the relational expression K = Gamma epsilon/N-2. The dissipation flux coefficient Gamma is often set to a constant value of 0.2, but this study of LES revealed that Gamma varies greatly vertically in the bottom boundary layer because of the influence of the seabed. Consequently, the eddy diffusion coefficient is overestimated in the lower part of the bottom boundary, but it is slightly underestimated in the upper part. Therefore, Osborn's method with constant Gamma cannot give the correct diffusivity. Furthermore, even if treating Gamma as a function of flux Richardson number R-f, as defined originally by Osborn, the estimation is underestimated by the advection effect because of the influence of spatial nonuniformity. Energy budget analysis revealed that this defect can be improved using the extended flux Richardson number, which can be estimated by multiplying R-f using a constant correction factor. Furthermore, we proposed two alternative estimation methods. For the first method, which estimates the relation between R-f and the gradient Richardson number R-g, Gamma can be expressed with R-g instead of R-f with a correction factor. We can estimate the reasonable diffusivity if we have current data supplementary to obtain R-g. For the second method, Gamma can be expressed as a similarity function of the height above the bottom normalized by the Ozmidov scale. This method can provide an acceptable estimate of diffusivity without current data for several circumstances.