A fractional step method is developed for solving the time dependent two‐dimensional Euler equations with full non‐linear free‐surface boundary conditions. The geometry of the free surface is described by a height function, and its evolution is tracked by integrating in time the kinematic boundary conditions based on the free‐surface volume flux. The fluid domain is discretised by adapting a time‐varying curvilinear grid to all boundaries, including the free surface. Mass and momentum equations are discretised by a conservative finite volume formulation, taking into account the time dependency of the grid. A fractional step type method is developed for integrating the fluid motion in time. The method is applied to a non‐linear standing wave in a square container, testing for compliance with mass and energy conservation and comparing computed wave period with other results. Non‐linear travelling waves are simulated in channels with either constant depth or varying depth and non‐linear wave processes involving both triad interactions and quartet interactions are studied. Results are compared with both experimental data and theoretical results and excellent agreement is found. Interaction of waves and currents is studied. The blocking of waves in an opposing current is simulated and found to show good agreement with theoretical results. The method is intended to be a first step towards a full description of wave dynamics interacting with structures and currents. © 1998 John Wiley & Sons, Ltd.

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Interactions between surface waves and underlying viscous wake are investigated for a turbulent flow past a free surface piercing circular cylinder at Reynolds number Re=2.7×104 using large eddy simulation (LES). The computations have been performed for three Froude numbers Fr=0.2, 0.5 and 0.8 in order to examine the influence of the Froude number. A second-order finite volume method coupled with a fractional step method is used for solving the grid-filtered incompressible Navier-Stokes equations. The computational results are found to be in good agreement with the available experimental data. At low Froude numbers Fr=0.2 and 0.5, the amplitude of generated surface wave is small and the influence on the wake is not evident. On the other hand, strong wave-wake interactions are present at Fr=0.8, when the generated free surface wave is very steep. It is shown that structures of the underlying vortical flow correlate closely with the configuration of the free surface. Computational results show presence of a recirculation zone starting at the point where the surface slope changes discontinuously. Above this zone the surface elevation fluctuates intensively. The computed intensity of the surface fluctuation is in good agreement with the measurements. It is also shown that the periodic vortex shedding is attenuated near the free surface at a high Froude number. The region in which the periodic vortex shedding is hampered extends to about one diameter from the mean water level. It is qualitatively shown that the separated shear layers are inclined outward near the free surface due to the generation of the surface waves. This change in the relation between two shear layers is suggested to be responsible for the attenuation of the periodic vortex shedding.

A new third-generation spectral wave model is presented for prediction of the wave climates in offshore and coastal areas. The essential topic of the present paper is new numerical techniques for solution of the governing equations. The discretisation in the geographical space and the spectral space is based on cell-centred finite volume technique. In the geographical space, an unstructured mesh is applied. Due to the high degree of flexibility, unstructured meshes are very efficient to deal with problems of different characteristic scales. The time integration is performed using a fractional step approach, where an efficient multisequence explicit method is applied for the propagation process. The model is verified by comparison with observations for two real field cases.

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