A sigma-coordinate, primitive equation ocean circulation model is used to explore the problem of the remnant generation of trapped waves about a tall, circular, isolated seamount by an incident oscillatory barotropic current. The numerical solutions are used to extend prior studies into the fully nonlinear regime, and in particular to quantify and interpret the occurrence of residual circulation. Specific attention is also devoted to the dependence of the resonance and rectification mechanisms on stratification, forcing frequency, and choice of subgrid-scale viscous closure.
Resonantly generated trapped waves of significant amplitude are found to occur broadly in parameter space; a precise match between the frequency of the imposed incident current and the frequency of the trapped free wave is not necessary to produce substantial excitation of the trapped wave. The maximum amplification factors produced in these numerical solutions, O(100) times the strength of the incident current, are consistent with previous studies.
In the presence of nonlinear advection, strong residual currents are produced. The time-mean circulation about the seamount is dominated by a strong bottom-intensified, anticyclonic circulation closely trapped to the seamount. Maximum local time-mean current amplitudes are found to be as large as 37% of the magnitude of the propagating waves. In addition to the strong anticyclonic residual flow, there is a weaker secondary circulation in the vertical-radial plane characterized by downwelling over the top of the seamount at all depths. Maximum vertical downwelling rates of several tens of meters per day occur at the summit of the seamount. The vertical mass flux implied by this systematic downwelling is balanced by a slow radial flux of mass directed outward along the flanks of the seamount.
Time-mean budgets for the radial and azimuthal components of momentum show that horizontal eddy fluxes of momentum are responsible for transporting net radial and azimuthal momentum from the far field to the upper flanks of the seamount. There, Coriolis and pressure gradient forces provide the dominant balances in the radial direction. However, the Coriolis force and viscous effects provide the primary balance for the azimuthal component.