Abstract
A new derivation of ray equations is proposed in the framework of a current uniform with depth, differentiating the contributions from the current-induced wave phase speed and wave group velocity. It is useful when substituting higher order expressions for those quantities that account for a sheared current. The new formulation is easy to implement in third-generation spectral wave models even if this task is not performed in the present paper. The numerical vertical integration of the current profile evaluating the current-induced corrections is also studied. We show that a large numerical error can potentially be induced if one uses the vertical resolution normally encountered in ocean modeling. We offer a simple solution to reduce this error and demonstrate its impact on the computation of the current-induced phase speed and wave group corrections using both theoretical and realistic profiles. Discrepancies can induce changes up to 40% of the current-induced speed. We observe these strong discrepancies for large wavenumbers, associated with wind waves, when current effects are the most prevalent.
Highlights
Storm events can lead to flooding and destruction of coastal human settlements
They used the coupled system COAWST (Coupled Ocean Atmosphere Wave Sediment Transport),2,3 where the ocean model ROMS (Regional Ocean Modeling System)4 interacts with the wave model SWAN (Simulating Waves Nearshore)
A more consistent derivation of the ray equations is shown as Eqs. (31)–(36), closed by Eqs. (28)–(30) for the current-induced terms
Summary
Storm events can lead to flooding and destruction of coastal human settlements. Waves play a key role by contributing to the storm surge and carrying energy that they eventually dissipate by breaking on nearshore and coastal infrastructures. Variations of the wave field in spectral space, introducing rates of change both in wave frequency and wave direction, form a significant gap between, for instance, the framework used in Banihashemi and Kirby and present wave models They are necessary for the latter as they solve the propagation of the wave action averaged over all directions and frequencies, but they do not appear in the previously mentioned studies as they all focus on monochromatic waves. Different methods are used to find solutions, such as the Wentzel–Kramers–Brillouin (WKB) approximations, or asymptotic developments, but the focus is always on the wave amplitude and not on the wave ray trajectories All these studies assumed a vertically uniform current. Through both analytical and realistic examples, we highlight its impact on the computation of the vertical integral
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