The coupled mode parabolic equation

The coupled mode parabolic equation (PE) is a generalization of the adiabatic mode PE that includes mode coupling terms. It is practical to apply this approach to large-scale problems involving coupling of energy between both modes and azimuths. The solution is expressed in terms of the normal modes and mode coefficients, which satisfy coupled horizontal wave equations. The coupled mode PE may be solved efficiently with the splitting method. The first step is equivalent to solving the adiabatic mode PE over one range step. The second step involves the integration of the coupling term. The coupling mode PE solution conserves energy, which is an important aspect of a range-dependent propagation model. The derivation of the coupled mode PE, which involves completing the square of an operator, is related to the derivation of an adiabatic mode PE that accounts for ambient flow. Examples are presented to illustrate the accuracy of the coupled mode PE.