A polar method for obtaining wave resonating quadruplets in finite depths

A polar method for obtaining wave resonating quadruplets {K1, K2, K3, K4} in the computation of nonlinear wave-wave interaction source term of the wave model is presented with results for both deep and finite water depths. The method first determines the end radial points of the locus equation for K2, for each set of input wave vectors (K1, K3) on the symmetry. The locus of K2 (and hence K4) is then traced in the anti-clockwise direction starting with the maximum radial point on the line of symmetry. It is shown that when k3>k1, the number of points on the locus varies when the orientations of the input wave vectors are changed and reduces when the difference in the magnitude of the input wave vectors is increased. A significant advantage in this method is that the angular increment on the locus for K2 can be kept constant.