Internal generation of waves for time-dependent mild-slope equations

Abstract

A technique for internal generation of waves is studied for two time-dependent mild-slope equation models developed by Copeland [Copeland, G.J.M., 1985. A practical alternative to the mild-slope wave equation. Coastal Eng., 9, pp. 125-149] and Radder and Dingemans [Radder, A.C., Dingemans, M.W., 1985. Canonical equations for almost periodic, weakly nonlinear gravity waves. Wave Motion, 7, pp. 473-485]. For the Radder and Dingemans' equations, desired energy of incident waves could not be obtained from the viewpoint of mass transport which has successfully been used for the Boussinesq equations and the Copeland equations by Larsen and Dancy [Larsen, J., Dancy, H., 1983. Open boundaries in short wave simulations-a new approach. Coastal Eng., 7, pp. 285-297] and Madsen and Larsen [Madsen, P.A., Larsen, J., 1987. An efficient finite-difference approach to the mild-slope equation. Coastal Eng., 11, pp. 329-351], respectively. However, for both of the Copeland's and Radder and Dingemans' models, desired energy of incident waves could be obtained from the viewpoint of energy transport. Using the viewpoint of energy transport in the Radder and Dingemans equations, which treat random waves of narrow frequency band properly, we could successfully generate not only monochromatic waves but also directional random waves. (C) 1998 Elsevier Science B.V. All rights reserved.