A weakly nonlinear coupled-mode model for wave-current-seabed interaction over general bottom topography

• Main Authors: Belibassakis, KA, Gerostathis, ThP, Athanassoulis, GA
• Format: Conference Object
• Language: unknown
• Published: 2008
• Subjects: Analytical structure; Bottom boundary conditions; Bottom topography; Coupled systems; Evanescent mode; Finite difference scheme; Horizontal planes; Nonlinear waves; Numerical results; One-equation model; Propagating mode; Scattered waves; Seabed interaction; Second orders; Steady current; Test case; Variational principles; Vertical distributions; Vertical modes; Wave current interaction; Wave potentials; Wave scattering; Arctic engineering; Boundary conditions; Mechanics; Ocean engineering; Topography; Variational techniques; Wave propagation; Wave equations; Arctic
• Online Access: http://dspace.lib.ntua.gr/handle/123456789/35546

A weakly nonlinear, coupled-mode model is developed for the wave-current-seabed interaction problem, with application to wave scattering by steady currents over general bottom topography. Based on previous work by the authors (Athanassoulis & Belibassakis [1], Belibassakis et al [2]), the vertical distribution of the scattered wave potential is represented by a series of local vertical modes containing the propagating mode and all evanescent modes, plus an additional term accounting for the bottom boundary condition when the bottom slope is not negligible. Using the above representation, in conjunction with Luke's [3] variational principle, the wave-current-seabed interaction problem is reduced to a coupled system of differential equations on the horizontal plane. If only the propagating mode is retained in the vertical expansion of the wave potential, and after simplifications, the present system is reduced to an one-equation model compatible with Kirby's [4] mild-slope model with application to the problem of wave-current interaction over slowly varying topography. The present coupled-mode system is discretized on the horizontal plane by using a second-order finite difference scheme and numerically solved by iterations. Numerical results are presented for two representative test cases, demonstrating the importance of the first evanescent modes and the sloping-bottom mode. The analytical structure of the present model facilitates its extension to treat fully non-linear waves, and it can be further elaborated to study wave propagation over random bottom topography and general currents. Copyright © 2008 by ASME.