Let us comment briefly how the ener

Let us comment briefly how the energy balance equation is obtained. Consider first the case that there are no sources and sinks, hence S = 0. In this ideal case, surface gravity waves are a Hamiltonian system [23,24] and the equations of motion follow from a variational principle which minimizes the surface pressure. A straightforward application of Whitham’s average variational principle then results (see e.g. [25,26]) in the vanishing of the left-hand side of the energy balance equation (called the adiabatic part). Therefore, in the absence of sources and sinks there are only two reasons why the wave spectrum changes in time,