The Role of Western Boundary Layers in Gyre Scale Ocean Mixing

Abstract

A variety of two-dimensional advection-diffusion models are investigated analytically with the goal of understanding the role of boundary layer in gyre-scale ocean mixing. It is assumed throughout that the Péclet number of the flow in the Sverdrup interior, Pe = UL/k is large. (Here, L) is the length of the gyre, U is the velocity scale in the interior and k is the explicit diffusivity.) There are then two limits depending on the size of (I/L) where l is the width of the western boundary layer. First, if (I/L)P is large, the diffusion is weak everywhere in the gyre and the tracer makes repeated passages through the boundary layer before mixing. In this case, the time taken to mix is (Ll/k). Second, if (l/L)P is small, the diffusion is strong in the boundary layer and the time taken to mix is the circulation time L/U. In any case, the mixing time is substantially less than the diffusion time based on the length scale of the gyre.