A New Solution of a Nonlinear Model of Upwelling

A two-dimensional, frictionless, nonlinear model of coastal upwelling is reexamined. The model has been solved previously at steady state and as an initial-value problem. The previous solution to the initial-value problem is inconsistent with the steady-state solution. A new solution to the spinup problem is presented that approaches the existing steady-state solution. In the new solution, a surface equatorward jet develops more rapidly than a poleward undercurrent, but the surface jet is of limited strength so that the undercurrent velocity eventually surpasses that of the surface flow. Consideration of dimensional scales implies that the magnitude of the wind stress determines how quickly steady state is approached but does not affect the steady-state fields. Exact solutions found with an arbitrary alongshore pressure gradient imply that there is no poleward flow without a poleward pressure gradient.