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Results of numerical investigations, based on full dynamic equations, are presented for wave breaking in one-dimensional environment with wave spectrum. The breaking is defined as a process of irreversible collapse of an individual wave in physical space, and the incipient breaker is a wave which reached a dynamic condition of the limiting stability where the collapse has not started yet, but is inevitable. Main attention is paid to documenting the evolution of different wave characteristics before the breaking commences. It is shown that the breaking is a localized process which rapidly develops in space and time. No characteristics such as wave steepness, wave height, and asymmetry can serve as a predictor of the incipient breaking. Process of breaking is intermittent; it happens spontaneously and is individually unpredictable. Evolution of geometric, kinematic, and dynamic characteristics of the breaking wave describes the process of breaking itself rather than indicating an imminent breaking. It is shown that the criterion of breaking, valid for the breaking due to modulation instability in one-dimensional wave trains, is not universal if applied to the conditions of spectral environment. In this context, more important is development of algorithms for parameterization of breaking for wave prediction models and for direct wave simulations. Prototype of such algorithm is proposed on the basis of the diffusion-type highly selective operator. It is suggested that the main parameter is differential steepness calculated over entire spectrum. Thousands of exact short-term simulations of evolution of two superposed wave trains with different steepness and wave numbers were performed to investigate the effect of wave crests’ merging. Nonlinear sharpening of the merging crests is demonstrated. It is suggested that such effect may be responsible for the appearance of the typical sharp crests of surface waves, as well as for wave breaking.
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- Numerical Investigation of Wave Breaking
Dmitry V. Chalikov
- Chapter 8