Numerical modeling of surface wave development under the action of wind

Abstract

Abstract. The numerical modeling of two-dimensional surface wave development under the action of wind is performed. The model is based on three-dimensional equations of potential motion with a free surface written in a surfacefollowing nonorthogonal curvilinear coordinate system in which depth is counted from a moving surface. A threedimensional Poisson equation for the velocity potential is solved iteratively. A Fourier transform method, a secondorder accuracy approximation of vertical derivatives on a stretched vertical grid and fourth-order Runge-Kutta time stepping are used. Both the input energy to waves and dissipation of wave energy are calculated on the basis of earlier developed and validated algorithms. A one-processor version of the model for PC allows us to simulate an evolution of the wave field with thousands of degrees of freedom over thousands of wave periods. A long-time evolution of a twodimensional wave structure is illustrated by the spectra of wave surface and the input and output of energy.

Spatial evolution of young wind waves: numerical modelling verified by experiments

“…Fully nonlinear methods are often applied to study the temporal evolution of unidirectional waves in general, and of wind waves in particular (see e.g. Chalikov 2018); that paper also contains a review of additional studies. These methods are clearly inapplicable for modelling of the variation of statistically stationary random waves propagating in the wind direction that are inhomogeneous and non-periodic in space.…”

High-Resolution Numerical Simulation of Surface Wave Development under the Action of Wind

“…We consider these results as a serious evidence of high accuracy of the adiabatic version of the model. The previous version of 3-D model [26] allowed carrying out a long simulation of Stokes wave not steeper than AK ¼ 0:30. The right-hand sides of Eqs.…”

“…The equation for the potential was solved at each of the four substeps of time step. The simulations described by Chalikov [26] were a first attempt to reproduce the development of wave field assigned in the initial conditions as a group of small waves at high wave number under the action of strong wind. The initial elevation was generated as a superposition of linear waves corresponding to JONSWAP spectrum [29] with random phases.…”

“…The detailed description of the algorithm for calculation of energy input is given in Ref. [26]. The energy and momentum are transferred from air to water by the surface pressure field and tangent stress.…”

“…Hence, the full problem of wave evolution should be formulated on the basis of three-dimensional equations. Such 3-D calculations were done by Chalikov [26]. The model included parameterization of the main physical processes: input energy, different types of dissipation, and transformation of spectrum due to the nonlinear interaction.…”