Energy and pseudoenergy flux in the internal wave field generated by tidal flow over topography

The mechanical energy and pseudoenergy budgets in the internal wave field generated by tidal flow over topography is considered using a nonlinear, two-dimensional numerical model. The Boussinesq and rigid lid approximations are made, viscosity and diffusion are ignored and the flow is treated as incompressible. Both ridge and bank edge topographies are considered. The nonlinear energy equation and an equation for pseudoenergy (kinetic energy plus available potential energy) are satisfied to within less than 1%. For a uniform stratification (constant buoyancy frequency N  ) the available potential energy density is identical to the linear potential energy density 12(g2/N2)ρ˜d2 where ρ˜d is the density perturbation. For weak tidal flow over a ridge in the deep ocean, using a uniform stratification, the generated waves are small, approximately 2% of the water depth, and the traditional expression for the energy flux, 〈u˜p˜d〉 accurately gives the pseudoenergy flux. For a case with strong tidal flow across a bank edge, using a non-uniform stratification, large internal solitary waves are generated. In this case, the linear form of the potential energy is very different from the available potential energy and the traditional energy flux term 〈u˜p˜d〉 accounts for only half of the pseudoenergy flux. Fluxes of kinetic and available potential energy are comparable to the traditional energy flux term and hence must be included when estimating energy fluxes in the internal wave field.