Linear and Nonlinear Wave Action Estimates

The effects of nonlinearities on wave action quantities computed for irrotational surface gravity waves propagating on an inviscid incompressible fluid may be demonstrated on the relative wave steepness-relative water depth dissection plane by contours of relative errors between estimates computed by the nonlinear Dean Stream Function and by linear wave theory. The relative errors for energy density quantities and the ratio of nonlinear wave length values to linear wave length values are found to increase monotonically in magnitude with increasing relative wave steepness and with increasing Ursell number. A contour of zero relative error which intersects the breaking index in intermediate water depth and a positive extremal of relative error in deep water are found on the dissection plane for the average total energy flux estimates.