LES Study of Vertical Eddy Diffusivity Estimation in Bottom Boundary Layers

Abstract

Osborn’s method is commonly used to obtain diffusion coefficient K from the turbulent dissipation rate ε. This method is the relational expression . The dissipation flux coefficient is often set to a constant value of 0.2, but this study of LES revealed that 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 cannot give the correct diffusivity. Furthermore, even if treating as a function of flux Richardson number , 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 using a constant correction factor. Furthermore, we proposed two alternative estimation methods. For the first method, which estimates the relation between and the gradient Richardson number , can be expressed with instead of with a correction factor. We can estimate the reasonable diffusivity if we have current data supplementary to obtain . For the second method, 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.

Interactions of Remotely Generated Internal Tides With the U.S. West Coast Continental Margin

“…However, in the mixed layer and near the seabed, we obtain unrealistically high diffusivity estimates when Γ is set to a constant value of 0.2. In the boundary layers, we calculate the mixing efficiency as (Wakata, 2018) $$${\Gamma }=\frac{\chi R{i}_{g}}{1-\chi R{i}_{g}},$$$ where Ri g is the gradient Richardson number $$\left(\frac{{N}^{2}}{{\left(\frac{\partial {u}^{\prime }}{\partial z}\right)}^{2}+{\left(\frac{\partial {v}^{\prime }}{\partial z}\right)}^{2}}\right)$$ and χ = 1.79.…”

“…However, in the mixed layer and near the seabed, we obtain unrealistically high diffusivity estimates when Γ is set to a constant value of 0.2. In the boundary layers, we calculate the mixing efficiency as (Wakata, 2018)…”

Modelling the kinetic reactive transport of pollutants at the sediment-water interface. Applications with atmospheric fallout radionuclides

“…The vertical eddy diffusivity in the bottom boundary layer is still several orders of magnitude higher than the molecular diffusion (Wakata, 2018). Thus, assuming a sharp drop from eddy diffusivity above the SWI to only molecular diffusion just below it may not be a realistic description of the natural world.…”

Diapycnal mixing variations induced by subthermocline eddies observed in the north Pacific western boundary region

“…Diapycnal diffusivity representative of turbulent mixing rate is commonly estimated using the relationship k r =Gϵ/N 2 (Osborn, 1980), whereG is the mixing efficiency set to be 0.2. Note that it may be problematic using constant mixing efficiency in the mixed and bottom boundary layers (Lappe and Umlauf, 2016;Salehipour et al, 2016;Wakata, 2018;Monismith et al, 2018). However, this study focuses on the ocean interior (below the mixed layer and far away from the bottom boundary layer).…”