Two-dimensional study of Rossby waves generated by an initial disturbance

Abstract

Rossby waves are the fundamental time dependent large-scale motion of the ocean and atmosphere. In this article, we are interested to find analytical solution of Rossby waves produced by an initial disturbance. These waves, as we know, are archetypical low-frequency waves, which play a central role in defining meteorological and oceanographic conditions. Our purpose here is to analyze the properties of such waves in two dimension as a guide to the construction of the dynamical framework appropriate for low-frequency motion. As a precursor to our aim, we revisited the problem of Rossby wave generation in an ocean bounded by two imaginary latitudes for a particular type of external forcing. The characteristics of this motion are explored with the help of group velocity and phase velocity. Subsequently, the two-dimensional case of generation of Rossby wave by a general form of disturbance in an unbounded ocean is solved where the concept of stationary phase method is extensively used. The rules of governing the propagation of wave packet are discussed, and we found for a wave-like disturbance, Rossby wave is not a single wave train but rather several, which moves as a wave front with a definite direction-deviation. It is natural to question what role, if any, the source plays in explicit determination of these radiated waves and their asymptotic behavior. To address these and other concerns, we have developed an analytical model of generation of Rossby waves produced by an initial disturbance in two-dimensional open ocean with a considerable generality.