Curvilinear parabolic approximation for surface wave transformation with wave-current interaction

Journal Article · Sun Apr 10 04:00:00 EDT 2005 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2004.10.022· OSTI ID:20687226

Fengyan, Shi ^[1]; Kirby, James T ^[1]

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1. Center for Applied Coastal Research, Center for Applied Coastal Research, University of Delaware, Newark, DE 19716 (United States)

The direct coordinate transformation method, which only transforms independent variables and retains Cartesian dependent variables, may not be an appropriate method for the purpose of simplifying the curvilinear parabolic approximation of the vector form of the wave-current equation given by Kirby [Higher-order approximations in the parabolic equation method for water waves, J. Geophys. Res. 91 (1986) 933-952]. In this paper, the covariant-contravariant tensor method is used for the curvilinear parabolic approximation. We use the covariant components of the wave number vector and contravariant components of the current velocity vector so that the derivation of the curvilinear equation closely follows the higher-order approximation in rectangular Cartesian coordinates in Kirby [Higher-order approximations in the parabolic equation method for water waves, J. Geophys. Res. 91 (1986) 933-952]. The resulting curvilinear equation can be easily implemented using the existing model structure and numerical schemes adopted in the Cartesian parabolic wave model [J.T. Kirby, R.A. Dalrymple, F. Shi, Combined Refraction/Diffraction Model REF/DIF 1, Version 2.6. Documentation and User's Manual, Research Report, Center for Applied Coastal Research, Department of Civil and Environmental Engineering, University of Delaware, Newark, 2004]. Several examples of wave simulations in curvilinear coordinate systems, including a case with wave-current interaction, are shown with comparisons to theoretical solutions or measurement data.

• OSTI ID: 20687226
• Journal Information: Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: 2 Vol. 204; ISSN JCTPAH; ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CALCULATION METHODS
CARTESIAN COORDINATES
COMPARATIVE EVALUATIONS
COMPUTERIZED SIMULATION
CURVILINEAR COORDINATES
DIFFRACTION MODELS
MATHEMATICAL SOLUTIONS
TRANSFORMATIONS
VECTORS
WATER WAVES
WAVE EQUATIONS