The Attenuation of Vertically Propagating Internal Gravity Waves by a Randomly Varying Wind/Current Shear

Abstract

We consider the effect of a randomly varying horizontal advective flow on internal gravity waves propagating vertically in a nonrotating, stratified and unbounded fluid. Attention is focused on the alteration in the vertical growth rate for the waves when the background flow U is of the form U=Uo+?, where ? is a centered stationary random function of height (z) and Uo=constant. We show that for both long and short correlation lengths the randomness in the wind (or current) leads to a dissipation of wave energy such that the normal upward amplification of the waves can be significantly reduced. Similarly, the normal downward attenuation can be significantly enhanced. The alteration in phase speed produced by the random flow is also considered although it is not discussed in detail.