Effects of bottom relief in two-dimensional oceanic eddy diffusion models

Two-dimensional diffusion-reaction equation for a steady state, (∂/∂x)(K_x∂C/∂x) + (∂/∂z)(K_z∂C/∂z) - λC = 0, was used to investigate theoretically the effects of horizontal (K_x) and vertical (K_z) eddy diffusivities in the presence of bottom relief, on the concentrations of dissolved species transported by diffusional flux from sediments to the overlying water. Two types of the bottom relief, having dimensions comparable to the dimensions of the water column, were considered: (1) a basin, and (2) a continental shelf. In a basin, distribution of a dissolved species of short half-life (in the example used, ²²²Rn, half-life 3.8 days) is, as expected, strongly affected by the eddy diffusional structure of the water body: for a given bottom shape and vertical eddy diffusivity, a higher horizontal diffusivity produces distribution more uniform horizontally. However, estimates of K_z based on one-dimensional vertical concentration profiles, depend on the horizontal eddy turbulence (K_x) in the basin. For the water overlying continental shelf and slope, a model based on the ²²⁸Ra flux from sediments and eddy-diffusional anisotropy of the water, produces concentrations in the surface water comparable to the values reported in the literature. In general, steady-state concentrations of radionuclides (or reactive species) in diffusionally anisotropic bodies of water are affected by the topographic relief of the bottom.