Dynamics of surface and internal long waves generated by atmospheric pressure disturbances

Abstract

Different from non-dispersive wave models such as the shallow water equations, MCC (Miyata, Choi, and Camassa) type strongly nonlinear dispersive wave model can describe not only the dynamics of surface waves, but also those of internal waves. The MCC model for a two-layer fluid system is applied to study dynamics of both surface waves and internal waves. The resonance mechanisms with atmospheric pressure disturbances are numerically studied not only for surface waves, so-called Proudman resonance, but also for internal waves. Baroclinic internal waves are generated when the speed of the atmospheric pressure disturbance is comparable to the critical linear internal wave speed. We compare the amplitudes of generated internal waves to the resonance theory for surface waves. Although most baroclinic internal wave phenomena can be explained by this linear theory, the relative magnitudes of amplitudes for forced and free waves do not agree with the theory. In addition, sequentially generated surface waves with resonance are observed when the radius of the atmospheric pressure disturbance is small. Finally, the dynamics of both surface and internal waves over non-uniform bottom topography are discussed in terms of Froude numbers to understand how they propagate and interact with each other when the Proudman resonance condition is satisfied while they travel.