A MILD-SLOPE EQUATION AND ITS WAVE ACTION CONSERVATION FOR WAVE-CURRENT INTERACTIONS
波-流相互作用的缓坡方程及其波作用量守恒

When surface waves propagate from the open sea to the coastal waters, the ubiquitous wavecurrent interactions are affected strongly by bottom topography. Using Hamiltonian variational principle for water waves, a mild-slope equation for wave-current interactions over arbitrary depth in the near shore region is developed, including the second-order effects arising from a general changes of waves, currents and depths, reducing to some typical mild-slope type equations and leading to a generalized eikonal equation. It is shown that the wave action conservation holds for the mild-slope equation.