Internal tide generation at the continental shelf

Internal tides are generated as the surface tide flows over topography. Their dynamical significance is well-known, including important roles in vertical mixing and the global distribution of tidal friction. However, modelling of their generation remains a challenge, largely because of the detailed nature of the topography typically involved, and the small scales present in internal wave beams.

Here we use a linear model of three-dimensional hydrostatic stratified flow over arbitrary topography, which is ideal for simplified studies of internal tide generation. The model uses a modal decomposition of the vertical structure of the dynamical fields, which is carefully chosen so that the bottom boundary condition and free-surface condition are automatically satisfied. The problem is reduced to solving a coupled set of partial differential equations in two horizontal directions and time, for which a variety of standard techniques are available. There are no restrictions on the stratification, so both interfacial waves and internal wave beams can be simultaneously resolved. Typically only a few modes are needed to capture the bulk of the internal wave flux.

Here we use this technique to study internal tide generation at the continental slope. We consider both the response to long surface waves normally incident on a two-dimensional slope, and simple three-dimensional scenarios with forcing by a coastal Kelvin wave. In both cases we examine the spatial and temporal form of the internal wave drag on the surface tide, which is intimately related to the internal wave energy fluxes radiating from the topography. The dependence of these quantities on the topographic profile and stratification is discussed.