terms of the horizontal momentum M the above equations become: Component form in Cartesian coordinates In a Cartesian coordinate system, the mass conservation equation becomes: with x and y respectively the x and y components of the mass transport velocity . The horizontal momentum equations are: Energy conservation For an inviscid flow the mean mechanical energy of the total flow – that is the sum of the energy of the mean flow and the fluctuating motion – is conserved. However, the mean energy of the fluctuating motion itself is not conserved, nor is the energy of the mean flow. The mean energy E of the fluctuating motion (the sum of the kinetic and potential energies satisfies: where ":" denotes the double-dot product, and ε denotes the dissipation of mean mechanical energy (for instance by wave breaking). The term is the exchange of energy with the mean motion, due to wave–current interaction. The mean horizontal wave-energy transport ( + cg) E consists of two contributions: E : the transport of wave energy by the mean flow, and cg E : the mean energy transport by the waves themselves, with the group velocity cg as the wave-energy transport velocity. In a Cartesian coordinate system, the above equation for the mean energy E of the flow fluctuations becomes: So the radiation stress changes the wave energy E only in case of a spatial-inhomogeneous current field (x,y). Notes References Primary sources Further reading Physical oceanography Water waves