Three-dimensional aspects of nonlinear stratified flow over topography near the hydrostatic limit

Steady, finite-amplitude internal-wave disturbances, induced by nearly hydr ostatic stratified flow over locally confined topography that is more elong ated in the spanwise than the streamwise direction, are discussed. The nonl inear three-dimensional equations of motion are handled via a matched-asymp totics procedure: in an 'inner' region close to the topography, the flow is nonlinear but weakly three-dimensional, while far upstream and downstream the 'outer' flow is governed, to leading order, by the fully three-dimensio nal linear hydrostatic equations, subject to matching conditions from the i nner flow. Based on this approach, non-resonant flow of general (stable) st ratification over finite-amplitude topography in a channel of finite depth is analysed first. Three-dimensional effects are found to inhibit wave brea king in the nonlinear flow over the topography, and the downstream disturba nce comprises multiple small-amplitude oblique wavetrains, forming supercri tical wakes, akin to the supercritical free-surface wake induced by linear hydrostatic flow of a homogeneous fluid. Downstream wakes of a similar natu re are also present when the how is uniformly stratified and resonant (i.e. the flow speed is close to the long-wave speed of one of the modes in the channel), but, in this instance, they are induced by nonlinear interactions precipitated by three-dimensional effects in the inner flow and are signif icantly stronger than their linear counterparts. Finally, owing to this non linear-interaction mechanism, vertically unbounded uniformly stratified hyd rostatic flow over finite-amplitude topography also features downstream wak es, in contrast to the corresponding linear disturbance that is entirely lo cally confined.