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