BOUSSINESQ TYPE EQUATIONS WITH HIGH ACCURACY IN DISPERSION AND NONLINEARITY

P.A. Madsen, B. Banijamali, H.A. Schaffer, O.R. Sorensen

Abstract


Two sets of Boussinesq type equations with high accuracy in dispersion as well as in nonlinearity are presented. The first set, which is expressed in terms of the depth-averaged velocity, includes up to fifth-derivative terms in the momentum equation, while the second set, which is expressed in terms of the velocity at an arbitrary z-level, includes up to third-derivative terms in the continuity equation as well as in the momentum equation. Both sets of equations provide linear dispersion characteristics, which are accurate for wave numbers (kh) up to 6, and nonlinear characteristics which are superior to previous Boussinesq formulations. The high quality of dispersion is also achieved for the Doppler shift in connection with wave-current interaction. A numerical model based on the new equations in two horizontal dimensions is presented and verified with respect to nonlinear transformation of waves in shallow water and refraction-diffraction in deep and shallow water.

Keywords


dispersion; nonlinearity; Boussinesq equation

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