Giovanna Vittori

The oscillating motion generated by a propagating surface wave over the bottom surface develops a bottom boundary layer whose dynamics is also of oscillating nature. The evaluation of the velocity field occurring close to the bottom is of particular importance, since it allows for a more accurate evaluation of the bottom shear stresses developing between the fluid and the bottom. Such stresses are relevant for, e.g., sediment mobilization and subsequent seabed modifications, as well as wave attenuation/dissipation over smooth and rough beds. The present contribution focuses on a suite of experimental tests performed at the Hydraulics and Maritime Engineering laboratory of Università Politecnica delle Marche (Ancona, Italy). In such experiments, Lagrangian and Eulerian velocity flow fields under progressive monochromatic surface waves over smooth and rough bottoms were obtained through particle tracking over the water column.

The velocity field within the bottom boundary layer generated by a propagating surface wave is quite important because it allows to determine the bottom shear stress, which is relevant from a practical point of view since, for example, it allows to verify whether the sediments, which make up the bottom, are set into motion and transported by the flow. If the surface wave is of small amplitude and the sea bottom is assumed to be smooth, the flow in the bottom boundary layer was determined by Stokes (1851) and Longuet-Higgins (1953), who showed that weak nonlinear effects generate a steady streaming. Laboratory experiments by Sleath (1988) showed that a laminar flow over a rough bottom made up of medium sand can be observed up to values of the Reynolds number equal to about 250. Therefore, real situations exist such that the flow regime is laminar and the bottom can be considered hydrodynamically rough. Recently, Blondeaux and Vittori (2023) proposed a simplified model for the oscillating boundary layer close to a rough bottom and derived the solution of the linearized problem. In the present contribution their model is used to solve the problem assuming weak non-linear effects, thus extending the solution by Longuet-Higgins (1953) to the more realistic case of rough bottom.

The sea surface can be described by means of the superposition of many sinusoidal functions. However, quite often the amplitude of each component turns out to be much smaller than its wavelength, and any component evolves independently of the others. Hence, it is common to investigate the dynamics of a simple monochromatic surface wave. Hereinafter, the flow generated by a monochromatic surface wave within the bottom boundary layer over a rippled sea bed is determined by means of the numerical integration of vorticity and continuity equations. The forcing term that drives the fluid motion within the boundary layer is evaluated assuming that the steepness of the monochromatic surface wave is much smaller than one and considering the first term of the Stokes expansion. Even though the irrotational flow that forces the viscous rotational flow near the sea bottom is symmetric with respect to the ripple crests, Blondeaux and Vittori [“A route to chaos in an oscillatory flow: Feigenbaum scenario,” Phys. Fluids A 3(11), 2492–2495 (1991a)] showed that the symmetry of the flow field is broken when the Reynolds number becomes larger than a threshold value Rδ,t1 that depends on the geometrical characteristics of the ripples. The results of Blondeaux and Vittori [“A route to chaos in an oscillatory flow: Feigenbaum scenario,” Phys. Fluids A 3(11), 2492–2495 (1991a)] suggest that, when the Reynolds number is larger than Rδ,t1 but not too far from it, a steady current is also generated. Hereinafter, the steady velocity component is determined as a function of the ripple characteristics.

The steady streaming generated by nonlinear effects at the bottom of a propagating surface wave is determined when the bottom is characterized by a roughness, the size of which scales with the boundary layer thickness. Therefore, the cornerstone contribution by Longuet-Higgins, who considered a smooth bottom, is extended to sea waves and sandy bottoms characterized by a grain size that ranges from fine silt to fine gravel. For values of the grain size d* up to 0.05δ*, δ* being the thickness of the viscous bottom boundary layer, the velocity profile is practically coincident with that predicted by Longuet-Higgins. If the grain size is further increased, the steady velocity component becomes larger and reaches a maximum value that is approximately 70% larger than that predicted by Longuet-Higgins. The maximum of the steady velocity component is attained for d*=0.6δ*. A further increase in d* leads to a decrease in the steady velocity component that, however, keeps always larger than that predicted for a smooth bottom. As the roughness size increases up to the values typical of medium sand, the steady velocity component increases. Then, a further increase in the roughness size leads to a decrease in the steady streaming even though, in the range of the roughness size presently investigated, the steady velocity component is always larger than that predicted for a smooth bottom.

Turbulence usually dominates the dynamics of water and air flows in a given fluid volume, or at least in a significant part of the flow field. The flow generated close to the sea bottom by propagat...

The oscillatory turbulent flow over two‐dimensional ripples is numerically simulated. Both the profile of the ripples and the values of the parameters used in the present study are typical of vortex ripples at the bottom of sea waves. The flow is computed numerically by using a RANSE approach. The results show that, as the ratio between the fluid excursion and the ripple wavelength is increased, the vortex shed on one side of the ripple crest is no longer the mirror image of the vortex shed on the other side and the dynamics of the vortex structures becomes quite complex. Moreover, the formation of steady recirculating cells, which might distort the profile of ripples in an erodible bed, is observed. A horizontal steady streaming is also generated, whose positive/negative direction depends on the values of the parameters.