Nonlinear inertia-gravity wave-mode interactions in three dimensional rotating stratified flows

Abstract

We investigate the nonlinear dynamics of inertia-gravity (IG) wave modes in threedimensional (3D) rotating stratified fluids. Starting from the rotating Boussinesq equations, we derive a reduced partial differential equation system, the GGG model, consisting of only wave-mode interactions. We note that this subsystem conserves energy and is not restricted to resonant wavemode interactions. In principle, comparing this model to the full rotating Boussinesq system allows us to gauge the importance of wave-vortical-wave vs. wave-wave-wave interactions in determining the transfer and distribution of wave-mode energy. As in many atmosphere-ocean phenomena we work in a skewed aspect ratio domain H/L (H and L are the vertical and horizontal lengths) with Fr = Ro < 1 such that Bu = 1, where Fr, Ro, and Bu are the Froude, Rossby, and Burger numbers, respectively. Our focus is on the equilibration of wave-mode energy and its spectral scaling under the influence of random large-scale (kf ) forcing. We present results from two sets of parameters: (i) Fr = Ro ≈ 0.05, H/L = 1/5, and (ii) Fr = Ro ≈ 0.1, H/L = 1/3. As anticipated from prior work, when forcing is applied to all modes with equal weight, with Fr = Ro ≈ 0.05 and H/L = 1/5, the wave-mode energy of the full system equilibrates and its spectrum scales as a power-law that lies between k-1 and k-5/3 for kf < k