On the possibility of biphase parametrization for wave transformation in the coastal zone

Abstract

Based on experimental data, we study the possibility of parametrizing the spatial variation in the phase shift (biphase) between the first and second nonlinear harmonics of wave motion during wave transformation over an inclined bottom in the coastal zone. It is revealed that the biphase values vary in the range [–π/2, π/2]. Biphase variations rigorously follow fluctuations in amplitudes of the first and second harmonics and the periodicity of energy exchange between them. Wave breaking influences the biphase value, retaining its variations in the negative domain in the range [–π/2, 0]. The formula applied in modern practice to calculate the biphase, which depends on the Ursell number, is incorrect for calculating the biphase for wave evolution in the coastal zone, because it does not take into account periodic energy exchange between the nonlinear harmonics. We propose a linear approximation of the biphase values from the size of the ratio of the current distance to the coast to the possible spacial duration of the exchange period, which is determined by the dispersion relation. We reveal the dependence of biphase variations on the wave transformation scenario and demonstrate the possibility of constructing a separate parameterization of the biphase for each scenario. Our research and the obtained biphase parameterizations can be used to simulate the sea state in the coastal zone, as well as in problems of predicting the development of coasts under the impact of storm waves.