PV-Induced Forcing of Gravity Waves in a Shallow Water Model

The influence of a geostrophically balanced or potential vorticity (PV) background flow on gravity wave propagation is examined using a rotating shallow water model. The system is analyzed in the context of a perturbative expansion that focuses on the dynamics of the resonances within the nonlinear terms of the system. The nonlinearity is reconstructed as a wave-wave interaction forcing on an otherwise undisturbed linear wavefield. The principal conclusion is that while the PV flow is generally undisturbed by the gravity wavefield, the gravity wavefield is forced by the geostrophic flow over moderate timescales. We numerically test these results for the interaction between a single geostrophic mode and a gravity wave, followed by propagation of a single gravity mode through a turbulent PV background. We find that the gravity mode energy is scattered into other modes of similar wavelength but different directions of propagation. The rate of dispersion is in agreement with resonant triad theory, where the rate depends primarily on the initial gravity wavenumber and background PV strength. These results are expected to have relevance to the propagation of coherent internal tides in the open ocean.}