The flow generated by the breaking of free-surface waves of different initial steepnesses is simulated numerically. The aim is to investigate the role played by the breaking intensity on the resulting flow. The study, which assumes a two-dimensional flow, makes use of a two-fluids Navier–Stokes solver combined with a Level-Set technique for the interface capturing. The evolution of periodic wavetrains is considered. Depending on the initial steepness ϵ, the wavetrain remains regular or develops a breaking, which can be either of spilling or plunging type. From the analysis of the local strain fields it is shown that, in the most energetic phase of plunging breaking, dissipation is mainly localized about the small air bubbles generated by the fragmentation of the air cavity entrapped by the plunging of the jet. The downward transfer of the horizontal momentum is evaluated by integrating the flux of momentum through horizontal planes lying at different depths beneath the still water level. From weak to moderate breaking, increase in the breaking intensity results in growing transfer of horizontal momentum, as well as thickening of the surface layer. Beyond a certain breaking intensity, the larger amount of air entrapped causes a reduction in the momentum transferred and the shrinkage of the layer. Quantitative estimates of the amount of air entrapped by the breaking and of the degassing process are provided. A scaling dependence of the amount of air entrapped by the first plunging event on the initial steepness is found. A careful analysis of the circulation induced in water by the breaking process is carried out. It is seen that in the plunging regime the primary circulation induced by the breaking process scales with the velocity jump between the crest and the trough of the wave.The limits of the main assumptions of the numerical calculations are analysed. It is shown that up to half-wave period after the breaking onset, the Reynolds number of the simulation does not significantly affect the solution. In order to further support the findings, an estimate of the uncertainty of the numerical results is derived through several repetitions of the numerical simulation with small perturbations of the initial conditions.

The self-similar solution that characterizes the water impact, with a constant vertical velocity, of a wedge entering the free surface with an arbitrary orientation is derived analytically. The study is carried out by assuming the fluid to be ideal, weightless and with negligible surface tension effects. The solution is based on the complex analysis of nonlinear two-dimensional problems of unsteady free boundary flows and is written in terms of two governing functions, which are the complex velocity and the derivative of the complex potential defined in a parameter domain. The boundary value problem is reduced to the system of an integral and an integro-differential equation in terms of the velocity modulus and of the velocity angle to the free surface, both written as functions of a parameter variable. The system of equations is solved through a numerical procedure which is validated in the case of symmetric wedges. Comparisons with data available in literature are established for this purpose. Results are presented in terms of free surface shape, contact angles at the intersection with the wedge boundary, pressure distribution, force and moment coefficients. For a given wedge angle, the changes induced by the heel angle on the above quantities are discussed. A criterion is proposed to determine the limit conditions beyond which flow separation from the wedge apex occurs. Comparisons with experimental results available in literature are presented.

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The liquid flow and the free surface shape during the initial stage of flat plate impact onto liquid half-space are investigated. Method of matched asymptotic expansions is used to derive equations of motion and boundary conditions in the main flow region and in small vicinities of the plate edges. Asymptotic analysis is performed within the ideal and incompressible liquid model. The liquid flow is assumed potential and two dimensional. The ratio of the plate displacement to the plate width plays the role of a small parameter. In the main region the flow is given in the leading order by the pressure-impulse theory. This theory provides the flow field around the plate after a short acoustic stage and predicts unbounded velocity of the liquid at the plate edges. In order to resolve the singular flow caused by the normal impact of a flat plate, the fine pattern of the flow in small vicinities of the plate edges is studied. It is shown that the initial flow close to the plate edges is self-similar in the leading order and is governed by nonlinear boundary-value problem with unknown shape of the free surface. The Kutta conditions are imposed at the plate edges, in order to obtain a nonsingular inner solution. This boundary-value problem is solved numerically by iterations. At each step of iterations the ''inner'' velocity potential is calculated by the boundary-element method. The asymptotics of the inner solution in both the far field and the jet region are obtained to make the numerical algorithm more efficient. The numerical procedure is carefully verified. Agreement of the computed free surface shape with available experimental data is fairly good. Stability of the numerical solution and its convergence are discussed.

The breaking of free surface waves is investigated numerically via a Navier‐Stokes model for the two‐fluids flow of air and water. Third order Stokes waves in a periodic domain are simulated. The fundamental wavelength is 27 cm, whereas the initial steepness varies from low values, leading to regular wave trains, up to artificially steep wave trains yielding plunging breaking events. Attention is focused on the early stage of the breaking, when most of the energy is dissipated. The energy content in air, the fraction associated to surface tension effects, the viscous dissipation in water, and the work done against the pressure field are analyzed in order to distinguish the different contributions to the dissipation. Vorticity fields and dissipation contours are also presented. In the spilling case, the extra energy content with respect to the steepest nonbreaking case focusses into the breaking region and is gradually dissipated. Once the extra energy has been dissipated, the resulting wave matches the steepest nonbreaking solution. In the plunging case, an important role is played by the air entrainment. A fraction between 10 to 35% of the energy dissipated by the breaking is spent in entraining the air cavity, and most of it is dissipated by viscous effects when the cavity collapses. The phenomenon is clearly highlighted by sequences of vorticity and dissipation contours. The circulation and the area of the cavity generated by the plunging of the jet are provided, and parametric dependencies are proposed.