A fully three-dimensional model is proposed for the generation of tidal sand waves and sand banks from small bottom perturbations of a flat seabed subject to tidal currents. The model predicts the conditions leading to the appearance of both tidal sand waves and sand banks and determines their main geometrical characteristics. A finite wavelength of both sand waves and sand banks is found around the critical conditions, thus opening the possibility of performing a weakly nonlinear stability analysis able to predict the equilibrium amplitude of the bottom forms. As shown by previous works on the subject, the sand wave crests turn out to be orthogonal to the direction of the main tidal current. The present results also show that in the Northern Hemisphere sand bank crests are clockwise or counter-clockwise rotated with respect to the main tidal current depending on the counter-clockwise or clockwise rotation of the velocity vector induced by the tide. Only for unidirectional or quasi-unidirectional tidal currents are sand banks always counter-clockwise rotated. The predictions of the model are supported by comparisons with field data. Finally, the mechanisms leading to the appearance of sand waves and sand banks are discussed in the light of the model findings. In particular, it is shown that the growth of sand banks is not only induced by the depth-averaged residual circulation which is present around the bedforms and is parallel to the crests of the bottom forms: a steady drift of the sediment from the troughs towards the crests is also driven by the steady velocity component orthogonal to the crests which is present close to the bottom and can be quantified only by a three-dimensional model. While the former mechanism appears to trigger the formation of counter-clockwise sand banks only, the latter mechanism can give rise to both counter-clockwise and clockwise rotated sand banks

Numerical simulations of Navier–Stokes equations are performed to study the flow originated by an oscillating pressure gradient close to a wall characterized by small imperfections. The scenario of transition from the laminar to the turbulent regime is investigated and the results are interpreted in the light of existing analytical theories. The ‘disturbed-laminar’ and the ‘intermittently turbulent’ regimes detected experimentally are reproduced by the present simulations. Moreover it is found that imperfections of the wall are of fundamental importance in causing the growth of two-dimensional disturbances which in turn trigger turbulence in the Stokes boundary layer. Finally, in the intermittently turbulent regime, a description is given of the temporal development of turbulence characteristics.

The dynamics of the vortex structures appearing in an oscillatory boundary layer (Stokes boundary layer), when the flow departs from the laminar regime, is investigated by means of flow visualizations and a quantitative analysis of the velocity and vorticity fields. The data are obtained by means of direct numerical simulations of the Navier–Stokes and continuity equations. The wall is flat but characterized by small imperfections. The analysis is aimed at identifying points in common and differences between wall turbulence in unsteady flows and the well-investigated turbulence structure in the steady case. As in Jimenez & Moin (1991), the goal is to isolate the basic flow unit and to study its morphology and dynamics. Therefore, the computational domain is kept as small as possible.The elementary process which maintains turbulence in oscillatory boundary layers is found to be similar to that of steady flows. Indeed, when turbulence is generated, a sequence of events similar to those observed in steady boundary layers is observed. However, these events do not occur randomly in time but with a repetition time scale which is about half the period of fluid oscillations. At the end of the accelerating phases of the cycle, low-speed streaks appear close to the wall. During the early part of the decelerating phases the strength of the low-speed streaks grows. Then the streaks twist, oscillate and eventually break, originating small-scale vortices. Far from the wall, the analysis of the vorticity field has revealed the existence of a sequence of streamwise vortices of alternating circulation pumping low-speed fluid far from the wall as suggested by Sendstad & Moin (1992) for steady flows. The vortex structures observed far from the wall disappear when too small a computational domain is used, even though turbulence is self-sustaining. The present results suggest that the streak instability mechanism is the dominant mechanism generating and maintaining turbulence; no evidence of the well-known parent vortex structures spawning offspring vortices is found. Although wall imperfections are necessary to trigger transition to turbulence, the characteristics of the coherent vortex structures, for example the spacing of the low-speed streaks, are found to be independent of wall imperfections.

[1] We describe a simple mathematical model capable of reproducing the main features of sand wave inception and growth. In particular we focus on the prediction of the migration rates that sand waves undergo because of tidal and residual currents. The model adequately predicts migration rates even for the cases of upstream-propagating sand waves, i.e., for sand waves which migrate in the direction opposite to that of the residual current. We show that upstream/downstream propagation is mainly controlled by the relative strength of the residual current with respect to the amplitude of the quarter-diurnal tide constituent and by the phase shift between the semi-diurnal and quarter-diurnal tide constituents. Therefore, to accurately predict field cases, a detailed knowledge of the direction, strength, and phase of the different tide constituents is required.

A linear stability analysis of the laminar flow in the boundary layer at the bottom of a solitary wave is made to determine the conditions leading to transition and the appearance of turbulence. The Reynolds number of the phenomenon is assumed to be large and a 'momentary' criterion of instability is used. The results show that the laminar regime becomes unstable during the decelerating phase, when the height of the solitary wave exceeds a threshold value which depends on the ratio between the boundary layer thickness and the local water depth. A comparison of the theoretical results with the experimental measurements of Sumer et al. (J. Fluid Mech., vol. 646, 2010, pp. 207-231) supports the analysis