Accelerated diffusion in the skewed shear flow of lake currents

Abstract

When the direction as well as the magnitude of the horizontal mean velocity (e.g., in a lake or ocean current) changes with the vertical coordinate, the horizontal diffusion of a batch of ‘marked’ fluid is greatly accelerated, as compared with diffusion in uniform flow. When, in addition, temporal changes are superimposed on this pattern, further dispersing effects appear. The net result is that, as observed during diffusion experiments in Lake Huron, apparent horizontal diffusivities increase steeply in complex currents. Theoretically some light may be thrown on this rather involved problem by several approximate measures: (1) by considering the kinematics of skewed, unsteady currents, (2) by calculating effective lateral or longitudinal diffusivities using a technique originated by G. I. Taylor in 1954, and (3) by calculating first and second moments of the concentration distribution in shear flow using the diffusion equation. Numerical estimates obtained in this manner of ‘acceleration’ effects show order of magnitude agreement with observations. From a practical point of view the interesting conclusion emerges that a low vertical eddy diffusivity tends to produce a high apparent horizontal diffusivity, owing to acceleration of diffusion by the greater complexity of the current, so that over-all dilution rates vary less than one would otherwise expect.