the intrinsic angular frequency. The action density plays the role of a number density
of waves, hence, apart from the ‘constant’ water density qw, the energy E of the waves is given by E ¼ rN,
while the wave momentum P is given by P ¼ kN.
For surface gravity waves evolving on a slowly varying current U in an ocean basin with slowly varying
depth D, the energy balance equation is given by