Two models of advection-diffusion in the oscillatory, sheared-velocity field of an internal wave are discussed. Our goal is to develop intuition about the role of such currents in horizontal ocean mixing through the mechanism of shear dispersion. The analysis suggests simple parameterizations of this process, i.e., those in Eqs. (7), (36) and (42). The enhanced horizontal diffusion due to the interaction of the vertical diffusion and vertical shear of the wave field can be described by an “effective horizontal diffusivity” which is equal to the actual horizontal diffusivity plus a term equal to the mean-square vertical shear of horizontal displacement times the vertical diffusivity, provided the vertical length scale of the horizontal velocity field is not too small. In the limit of small vertical length scale the expression reduces to Taylor's (1953) result in which the effective horizontal diffusivity is inversely proportional to the actual vertical diffusivity.

The solutions also incidentally illuminate a variety of other advection-diffusion problems, such as unsteady shear dispersion in a pipe and enhanced diffusion through wavenumber cascade induced by steady shearing and straining velocity fields.

These solutions also serve as models of horizontal stirring by mesoscale eddies. Simple estimates of mesoscale shears and strains, together with estimates of the horizontal diffusivity due to shear dispersion by the internal wave field, suggest that horizontal mesoscale stirring begins to dominate internal-wave-shear dispersion at horizontal scales larger than 100 m.