Turbulent Fluctuation and Transport of Passive Scalars by Random Wave Fields

Turbulent transport of passive scalars by random wave fields is studied, with applications to statistics of chlorophyll concentration in the ocean. The existence of the small parameter $u_0/c_0$, where $u_0$ and $c_0$ are the characteristic particle velocity and wave phase speed, respectively, allows essentially exact calculations, and as such provides a rich testing ground for quantitative comparisons between theory and observation. General expressions are derived for the diffusion constant and mean drift velocity. It is shown that the spectrum of passive scalar fluctuations displays at least two distinct inertial range power laws even when the wave velocity field has only one.