Wave-current interaction modeling incorporating wave blocking

One approach to the numerical modeling of wave-current interaction is by integration along characteristics. When the problem can be reduced to one dimension in both position and wavenumber, the computational load remains quite limited. In that type of modeling, however, wave blocking may occur, when the group speed of the wave being traced becomes equal but opposite to the local current. Simple ray tracing algorithms have to stop at that point. A different approach has been implemented, in which a dense set of characteristics in (wavenumber,position)-space is calculated by solving the characteristic equation of constant apparent frequency over a 1-dimensional positional grid. The resulting set contains both uninterrupted characteristics and ones that are terminated and created at the locations of wave blocking. Along these characteristics the action balance equation can be solved using a simple relaxation model. The action balance equation is integrated in a forward direction in the regions where the net velocity of the wave energy (group speed plus current velocity) is positive, and backward where it is negative. The resulting wave spectrum may be used as input for radar backscattering models