Weakly nonlinear oscillatory flow over an isolated seamount

Numerical models can show large errors in the modelling of flow around tall topography. We present a weakly nonlinear analytical solution of barotropic oscillatory flow over a tall axisymmetric seamount and compare the results to a numerical tidal model. The comparison is formulated for a flat topped seamount with parabolic sides and for a standing wave boundary condition in order to make the problem analytically tractable and to reduce it to a series of ordinary differential equations. The comparison shows reasonable agreement within the confines of the analytical formulation confirming that the numerical model can exploit tall topography. Comparisons to a Gaussian seamount and Kelvin wave forcing illustrate the generality of the results. The analytical formulation produces an equation relating relative errors in the comparison to discontinuities in topographical slope; the numerical model should have smaller errors over smoother topography. Residual velocities are found to be proportional to the aspect ratio of the topography.