The process which leads to the appearance of three-dimensional vortex structures in the oscillatory flow over two-dimensional ripples is investigated by means of direct numerical simulations of Navier–Stokes and continuity equations. The results by Hara & Mei (1990a), who considered ripples of small amplitude or weak fluid oscillations, are extended by considering ripples of larger amplitude and stronger flows respectively. Nonlinear effects, which were ignored in the analysis carried out by Hara & Mei (1990a), are found either to have a destabilizing effect or to delay the appearance of three-dimensional flow patterns, depending on the values of the parameters. An attempt to simulate the flow over actual ripples is made for moderate values of the Reynolds number. In this case the instability of the basic two-dimensional flow with respect to transverse perturbations makes the free shear layer generated by boundary layer separation become wavy as it leaves the ripple crest. Then the amplitude of the waviness increases and eventually complex three-dimensional vortex structures appear which are ejected in the irrotational region. Sometimes the formation of mushroom vortices is observed.

Numerical simulations of wall-bounded acceleration-skewed oscillatory flows are here presented. The relevance of this type of boundary layer arises in connection with coastal hydrodynamics and sediment transport, as it is generated at the bottom of sea waves in shallow water. Because of the acceleration skewness, the bed shear stress during the onshore half-cycle is larger than in the offshore half-cycle. The asymmetry in the bed shear stress increases with increasing acceleration skewness, while an increase of the Reynolds number from the laminar regime causes the asymmetry first to decrease and then increase. Low- and high-speed streaks of fluid elongated in the streamwise direction emerge near the wall, shortly after the beginning of each half-cycle, at a phase that depends on the flow parameters. Such flow structures strengthen during the first part of the accelerating phase, without causing a significant deviation of the streamwise wall shear stress from the laminar values. Before the occurrence of the peak of the free stream velocity, the low-speed streaks break down into small turbulent structures causing a large increase in wall shear stress. The ratio of the root-mean-square (r.m.s.) of the fluctuations to the mean value (relative intensity) of the wall shear stress is approximately 0.4 throughout a relatively wide interval of the flow cycle that begins when breaking down of the streaks has occurred in the entire fluid domain. The acceleration skewness and the Reynolds number determine the phase at which this time interval begins. Both the skewness and the flatness coefficients of the streamwise wall shear stress are large when elongated streaks are present, while values of approximately 1.1 and 5.4 respectively occur just after breaking has occurred. The trend of both the relative intensity and the flatness of the spanwise wall shear stress are qualitatively similar to those of the wall shear in the streamwise direction. As a result of the acceleration skewness, the period-averaged Reynolds stress does not vanish. Consequently, an offshore directed steady streaming is generated which persists into the irrotational region.

[1] The hydrodynamics generated by a regular wave field perpendicularly superimposed to a steady current is investigated by means of laboratory experiments. The flow structure is analyzed by measuring the velocity profiles using a micro Acoustic Doppler Velocimeter. Three cases are considered: current only, waves only and waves plus current. Different bottom roughnesses are used, and the apparent roughness k s is estimated for each condition. In the presence of a small roughness, the superposition of the waves on the current causes an increase of the current velocities close to the bottom, thus generating a decrease of the apparent roughness with respect to the case of the current only. On the other hand, when a large bottom roughness is present, the waves force a decrease of the current velocity close to the bottom and, in turn, an increase of the apparent bottom roughness. Such a behavior seems related not only to the roughness but also to the flow regime (i.e., laminar or turbulent) within the wave bottom boundary layer.

The turbulent flow generated by an oscillating pressure gradient close to an infinite plate is studied by means of numerical simulations of the Navier–Stokes equations to analyse the characteristics of the steady streaming generated within the boundary layer. When the pressure gradient that drives the flow is given by a single harmonic component, the time average over a cycle of the flow rate in the boundary layer takes both positive and negative values and the steady streaming computed by averaging the flow over n cycles tends to zero as n tends to infinity. On the other hand, when the pressure gradient is given by the sum of two harmonic components, with angular frequencies ω1 and ω2 = 2ω1, the time average over a cycle of the flow rate does not change sign. In this case steady streaming is generated within the boundary layer and it persists in the irrotational region. It is shown both theoretically and numerically that in spite of the presence of steady streaming, the time average over n cycles of the hydrodynamic force, acting per unit area of the plate, vanishes as n tends to infinity.

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