Abstract
Wave forecasting in ocean and coastal waters commonly relies on spectral models based on the spectral action balance equation. These models assume that different wave components are statistically independent and as a consequence cannot resolve wave interference due to statistical correlation between crossing waves, as may be found in, for instance, a focal zone. This study proposes a statistical model for the evolution of wave fields over non-uniform currents and bathymetry that retains the information on the correlation between different wave components. To this end, the quasi-coherent model (Smit & Janssen, J. Phys. Oceanogr., vol. 43, 2013, pp. 1741-1758) is extended to allow for wave-current interactions. The outcome is a generalized action balance model that predicts the evolution of the wave statistics over variable media, while preserving the effect of wave interferences. Two classical examples of wave-current interaction are considered to demonstrate the statistical contribution of wave interferences: (1) swell field propagation over a jet-like current and (2) the interaction of swell waves with a vortex ring. In both examples cross-correlation terms lead to development of prominent interference structures, which significantly change the wave statistics. Comparison with results of the SWAN model demonstrates that retention of cross-correlation terms is essential for accurate prediction of wave statistics in shear-current-induced focal zones.
Highlights
Wind-generated waves play an important role in the dynamics of oceanic and coastal waters
This study proposes a statistical model for the evolution of wave fields over non-uniform currents and bathymetry that retains the information on the correlation between different wave components
The corresponding change in the interference effect can be analysed from the physical point of view, by examining the correlation function, Γ, or from the spectral point of view, by considering the Wigner distribution, W
Summary
Wind-generated waves play an important role in the dynamics of oceanic and coastal waters. Surface waves can force large-scale circulations (e.g. Craik & Leibovich 1976), whereas near the shore they can drive alongshore currents Bowen 1969; Longuet-Higgins 1970; Reniers and Battjes 1997; Ruessink et al 2001), return flow (e.g. Dyhr-Nielsen & Sørensen 1970; Stive and De Vriend 1995) and associated sediment transport processes (e.g. Deigaard et al 1992; Van Rijn 1993).
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