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In the context of fluid flows, the coupled Ostrovsky equations arise when twodistinct linear long wave modes have nearly coincident phase speeds in thepresence of background rotation. In this paper, nonlinear waves in a stratifiedfluid in the presence of shear flow are investigated both analytically, usingtechniques from asymptotic perturbation theory, and through numericalsimulations. The dispersion relation of the system, based on a three-layermodel of a stratified shear flow, reveals various dynamical behaviours,including the existence of unsteady and steady envelope wave packets.

Coupled Ostrovsky equations for internal waves in a shear flow