Strongly nonlinear isotropic models for long internal waves in fluids of great depth

We are concerned with the nonlinear modelling of three-dimensional internal gravity waves in the lower atmosphere. A simplified configuration of density stratification is adopted, assuming that the atmosphere consists of two layers of uniform density with a sharp interface between the two bulk fluids. A time-dependent topography is considered to model a non-uniform, time-varying background current over variable terrain. Based on the Ablowitz–Fokas–Musslimani formulation for irrotational flows, both fully and weakly nonlinear long-wave isotropic models are derived in the Benjamin–Ono regime, where the upper layer is set to be semi-infinite. Two atmospheric gravity wave phenomena, motivated by satellite observations, are simulated using two modified numerical schemes to showcase the newly developed nonlinear models: the internal wave wake in the downwind zone behind a local topographic high and concentric ring waves, which appear as arched cloud formations along wave crests.