Nonlinear Interaction Between Vortex and Wave in Rotating Shallow Water

Abstract

This chapter is primarily concerned with the generation of inertia-gravity wave by vortical flows (spontaneous emission) in shallow water system on an f-plane. Sound waves are generated from vortical flows (aeroacoustics). There are many theoretical and numerical works regarding this subject. A shallow water system is equivalent to a twodimensional adiabatic gas system, if the effect of Earth's rotation is negligibly small. Then gravity waves are analogous to sound waves. While it is widely known that the effect of the Earth's rotation suppresses inertia-gravity wave radiation, there are few studies about spontaneous emission in rotating shallow water. Here, the generation of inertia-gravity waves by unsteady vortical flows is investigated analytically and numerically as an extension of aeroacoustics. A background of this subject is introduced briefly and several recent works including new results are reviewed. Main findings are cycloneanticyclone asymmetry in spontaneous emission and a local maximum of intensity of gravity waves emitted from anticyclones at intermediate value of the Coriolis parameter f, which are caused by the source originating in the Coriolis acceleration. All different experimental settings show the similar results, suggesting the robustness of these features.

Balance in non-hydrostatic rotating shallow-water flows

“…Balance has been an important theoretical concept, underlying the derivation of reduced sets of equations like quasigeostrophic [16][17][18] which have proved immensely fruitful. This concept has also enabled researchers to better understand the various ways nearly-balanced flows spontaneously emit inertia-gravity-waves [19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34] , or how imbalanced flows adjust to a nearly balanced state [35][36][37][38][39][40] . Balance has also been important practically, for example in estimating oceanic flow fields from limited data, [41][42][43][44] or in weather forecasting during data assimilation.…”