An energy-conserving two-way coupled mode model for underwater acoustic propagation

In order to avoid the energy non-conservation in two-way sound field calculations,which results from certain approximation of non-horizontal boundary,an energy-conserving twoway coupled mode propagation model is developed.During the derivation of this model,the non-horizontal boundary condition is treated strictly instead of making an approximation.The coupling equations,which are easy to numerical implementation,are derived from the equation of motion and the equation of continuity.Moreover,the validity of this model is illustrated with several numerical examples of different bottom parameters and the equation of energy conservation.It is shown that a boundary correction is introduced by the strict formulizing of the boundary condition in this model.This boundary correction guarantees the coupling coefficients being symmetrical and makes the sound fields satisfy the energy conservation.Thus,the energy-conserving coupled model is able to handle non-horizontal boundaries adequately,and the two-way sound fields in a non-horizontal stratified media can be calculated exactly by this model.