A few surprises in 2D nonlinear flow over topography

Nearly fifty years ago, R.R. Long demonstrated the surprising result that the steady, nonlinear streamfunction for stratified, 2D flow over topography could be obtained by the solution of a linear Helmholtz equation. Surprisingly, there are still new lessons which can be found in the margins of this now textbook example of topographic wave generation.

For example, it is generally believed that the boundary conditions for Long's solution introduce a hidden (and perhaps, nonlinear) complication. This turns out to be a myth, as general solutions can be obtained efficiently by restating the theory as a linear integral equation. Also addressible within this framework is the resolution of the singularities encountered when the topography has a net change of height. Finally, an analogous streamfunction theory when Coriolis effects are included will also be presented.