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The Evolution of Inhomogeneous Wave Statistics through a Variable Medium

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  • 1 Delft University of Technology, Delft, Netherlands
  • | 2 Theiss Research, El Granada, California
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Abstract

The interaction of ocean waves with variable currents and topography in coastal areas can result in inhomogeneous statistics because of coherent interferences, which affect wave-driven circulation and transport processes. Stochastic wave models, invariably based on some form of the radiative transfer equation (or action balance), do not account for these effects. The present work develops and discusses a generalization of the radiative transfer equation that includes the effects of coherent interferences on wave statistics. Using multiple scales, the study approximates the transport equation for the (complete) second-order wave correlation matrix. The resulting model transports the coupled-mode spectrum (a form of the Wigner distribution) and accounts for the generation and propagation of coherent interferences in a variable medium. The authors validate the model through comparison with analytic solutions and laboratory observations, discuss the differences with the radiative transfer equation and the limitations of this approximation, and illustrate its ability to resolve coherent interference structures in wave fields such as those typically found in refractive focal zones and around obstacles.

Corresponding author address: Pieter Smit, Environmental Fluid Mechanics, Faculty of Civil Engineering and Geosciences, Delft University of Technology, Stevinweg 1, 2628 CN Delft, Netherlands. E-mail: p.b.smit@tudelft.nl

Abstract

The interaction of ocean waves with variable currents and topography in coastal areas can result in inhomogeneous statistics because of coherent interferences, which affect wave-driven circulation and transport processes. Stochastic wave models, invariably based on some form of the radiative transfer equation (or action balance), do not account for these effects. The present work develops and discusses a generalization of the radiative transfer equation that includes the effects of coherent interferences on wave statistics. Using multiple scales, the study approximates the transport equation for the (complete) second-order wave correlation matrix. The resulting model transports the coupled-mode spectrum (a form of the Wigner distribution) and accounts for the generation and propagation of coherent interferences in a variable medium. The authors validate the model through comparison with analytic solutions and laboratory observations, discuss the differences with the radiative transfer equation and the limitations of this approximation, and illustrate its ability to resolve coherent interference structures in wave fields such as those typically found in refractive focal zones and around obstacles.

Corresponding author address: Pieter Smit, Environmental Fluid Mechanics, Faculty of Civil Engineering and Geosciences, Delft University of Technology, Stevinweg 1, 2628 CN Delft, Netherlands. E-mail: p.b.smit@tudelft.nl
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