A Preliminary Analytical Study on the Spontaneous Emission of Inertia gravity Waves from Vortical Flows

The emission of inertia gravity waves from the adjustment of balanced flows (or, basically, vortical flows) is currently regarded as a new mechanism of the pro duction of inertia gravity waves and referred as the spontaneous emission. Base d on f plane barotropic model, a preliminary analytical study on the spontaneou s emission of inertia gravity waves from vortical flows is conducted. First of all, the concept of slow manifold and balanced flow are discussed via this model and vortical property of the balanced flow is emphasized. Then, by assuming tha t the Froude number F and Rossby number satisfy and (implying that vortic al flow approximately balanced flow that includes gradient wind and other ageost rophic contributions), the basic equations are simplified to an inhomogeneous wa ve equation of inertia gravity wave, while the inhomogeneous term is related to the imbalance of the vortical flow. This inhomogeneous term vanishes when vorti cal flow is exactly balanced. So the imbalance of the vortical flow provides a f orcing or source to the inertia gravity wave. The Green function of this equa tion is found to give the inhomogeneous solution standing for the spontaneous em ission. In the field far from the wave "source", this inhomogeneous solution c an be expanded into far field form, including wave emission of monopole, dipole and quadrupole types. On the other hand, within or near to the "source" field, the near field form can serve as an approximate expression of the slow manifo ld. These results indicate that the convergence/divergence fields accompanied wi th vortical flows is composed of two main parts, i.e., the spontaneous emission o f inertia gravity waves from vortical flows and slow varying convergence/diver gence filed slaved to the adjustment of balanced flow. Although higher order ap proximation solution has already been given by Ford (2000) using method of match ed asymptotic expansions, the Green function solution can depict the spontaneo us emission in a more physical way.