Instability and breaking of internal waves in a horizontal shear flow

In the ocean interior, internal wave-mean flow interactions play a critical role in facilitating the transfer of energy from large to small scales. A classical model for wave breaking consists of a vertically propagating monochromatic wave incident on a vertical shear flow, resulting in small vertical scales and momentum and energy transfer to the mean flow near critical levels. Here, we study the orthogonal problem of a wave incident on a horizontal shear flow. The dynamics are fundamentally different from the classical scenario, with momentum and energy transferred from the mean flow to the wave near critical levels resulting in significant changes to the instability properties and subsequent turbulence. An extended linear WKB analysis reveals the role of two distinct perturbation growth mechanisms and allows for construction of a parameter space characterising the possible wave breaking dynamics of the initial state. Direct numerical simulations demonstrate the utility of the theory in the fully nonlinear regime. This work provides a natural link between wave breaking in vertically sheared flows and layered anisotropic stratified turbulence generated by purely horizontal motions, offering a deeper insight into observed patterns of mixing variability.