Application of a Coupled-Mode Theory for Wind-Wave Propagation Over an Idealized Cape-Related Shoal

Abstract:

Nearshore morphodynamics depends on wind wave transformation over the continental shelf. In regions of complicated bathymetry, we typically account for these transformations by applying weakly nonlinear wave theories. Here, we apply the 2D coupled-mode solution of Athanassoulis & Belibassakis (1999, J. Fluid Mech. 389) to explore wind-wave transformation cape-related nearshore bathymetry. Their solution uses a variational formulation of the linear wave transmission problem in 2D that includes propagating (forward and backward), evanescent, and sloping-bottom modes. We use an idealized bathymetric profile, h(x) in m, that represents an isolated shoal related to Cape Canaveral, USA, as

h(x) = -11.57 Si((x - 12.11/0.3125) + 1.65)+ 26.4283,

with x (in km) representing the relative distance across the shoal. The function resembles the overall morphology of Shoal E, offshore of Cape Canaveral: ~13 m depth at swales and ~5 m depth at ridge, ~1.5 km of length, and asymmetric onshore and offshore slopes. Incoming wave properties include the range of conditions found at Cape Canaveral, as given by Ur ∈ (10^-3, 10^-1) that transition to Ur ∈ (10^-2, 10^0) over the ridge. Analyses will explore the role of asymmetric slopes in the spatial variability in wave potential, which might support recent findings on isolated cape-related shoals providing a partial reflection mechanism to wind waves approaching cuspate forelands.