A Nonlinear Model of the Onset of Upwelling

A two-dimensional, non-dissipative, nonlinear model for the onset of upwelling is formulated. Consideration of the characteristic curves, which are complex, of the partial differential equation for the streamfunction leads naturally to the selection of new, characteristic coordinates in which the field equations become formally linear for the problem discussed. The new coordinate system is fundamentally similar to the one introduced by Hoskins and Bretherton in their study of atmospheric frontogenesis. As in the atmospheric case, the effect of nonlinearity sharpens the fields and inexorably reduces their scale below that of the deformation radius until a frontal discontinuity is formed.