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A three-dimensional parabolic equation model that includes the effects of rough boundaries
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1990
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Numerical AnalysisAeroacousticsEngineeringSurface WaveOceanographyMarine EngineeringComputational MechanicsHomogeneous Boundary ConditionComplex Sea StateNumerical SimulationShallow WaterNonlinear Hyperbolic ProblemHyperbolic EquationComputational GeophysicsMarine HydrodynamicsFree Boundary ProblemHyperbolic Conservation LawParabolic EquationRough BoundariesOcean EngineeringPhysical OceanographyCivil EngineeringMultiscale Modeling
A three-dimensional parabolic equation (3DPE) model that handles wide propagation angles in depth, narrow propagation angles in azimuth, and rough boundaries is derived and solved numerically with the method of alternating directions. A homogeneous boundary condition, which is easily incorporated into the numerical solution of the 3DPE, is applied at the ocean surface to approximate the effects of rough boundaries in terms of a reflection coefficient that depends on grazing angle. Calculations are presented to demonstrate the accuracy of the 3DPE and to demonstrate that horizontal coupling, the effects due to the term involving azimuth derivatives, can be important in shallow water (previous work has focused on deep-water applications). The model is applied to problems involving rough boundaries and range dependence.