Resonant over-reflection of waves by jets.

The present thesis studies the problem of scattering of large-scale waves by surface currents in the ocean. It has been known for more than a century that corresponding linear equations governing propagation of small amplitude waves across the shear flow contain critical layer singularities (Rayleigh [74]). And more than 40 years ago it was established that propagating waves can effectively interact with the mean flow at such points. As the result, the waves can be partly absorbed (Booker & Bretherton [8]) or over-reflected (i.e. amplified) (Jones [40]). A special case of this phenomenon, when amplification is infinitely strong, is traditionally referred to as resonant over-reflection. Physically the latter corresponds to spontaneous emission of waves by the current. Resonant over-reflection was poorly studied in the past with only a few cases reported in the literature. The aim of this study is to fill this gap and clarify the nature of the phenomenon. We examine scattering of inertia-gravity gravity waves by zonal currents within the reduced gravity rotating shallow water model and Rossby-wave scattering by “two-jet” currents on the quasi-geostrophic β-plane. In both cases reflection and transmission coefficients were calculated numerically for the case when mean flow velocity profiles are approximated by Bickley jets. Resonant over-reflection was found to occur within these two models. We proposed a plausible physical interpretation of the phenomenon as a “resonance” of a wave trapped between two containing potential barriers. It is further demonstrated that, generally, resonantly over-reflected waves are always marginal to radiating instabilities, and hence, indicate when unstable shear flows can generate temporally growing propagating waves that carry energy into the far field. The importance of the obtained results is connected to investigation of sources and distribution of waves in the ocean and atmosphere.