Passive scalar transport by travelling wave fields

We study turbulent transport of passive tracers by random wave fields of a rather general nature. A formalism allowing for spatial inhomogeneity and a nisotropy of an underlying velocity field (such as that caused by a latitud inally varying Coriolis parameter) is developed, with the aim of treating p roblems of large-scale ocean transport by long internal waves. For the spec ial case of surface gravity waves on deep water, our results agree with the earlier theory of Herterich & Hasselmann (1982), though even in that case we discover additional, off-diagonal elements of the diffusion tensor emerg ing in the presence of a mean drift. An advective diffusion equation includ ing all components of the diffusion tensor D plus a mean, Stokes-type drift u is derived and applied to the case of baroclinic inertia-gravity (BIG) w aves. This application is of particular interest for ocean circulation and climate modelling, as the mean drift, according to our estimates, is compar able to ocean interior currents; Furthermore, while on the largest (100 km and greater) scales, wave-induced diffusion is found to be generally small compared to classical eddy-induced diffusion, the two become comparable on scales below 10 km. These scales are near the present limit on the spatial resolution of eddy-resolving ocean numerical models. Since we find that u(z ) and D-zz vanish identically, net vertical transport is absent in wave sys tems of this type. However, for anisotropic wave spectra the diffusion tens or can have non-zero off-diagonal vertical elements, D-xz and D-yz, and it is shown that their presence leads to non-positive definiteness of D, and a negative diffusion constant is found along a particular principal axis. Ho wever, the simultaneous presence of a depth-dependent mean horizontal drift rc(z) eliminates any potential unphysical behaviour.