Non-hydrostatic layered flows over a sill

This work takes a new approach to solving non-hydrostatic equations of layered flows over bottom topography. A perturbation technique is used to find explicit expressions for a flow for different regimes of single- and two-layer flows over a sill. Excellent agreement with previous solutions and experimental data is obtained, and more details of the non-hydrostatic flow over a sill are revealed. The proposed method is simple and compact and removes the need for complex numerical techniques to solve the non-hydrostatic equations. It is shown that in the approach-controlled regime of two-layer flow over a sill, the flow upstream and farther downstream the sill crest can be described by the hydrostatic theory, and the flow is non-hydrostatic over only a short distance on the downstream side of the crest.