Wouter Kranenburg

Sand transport beneath waves: the role of progressive wave streaming and other free surface effects

Recent large-scale wave flume experiments on sheet-flow sediment transport beneath Stokes waves show more onshore-directed sediment transport than earlier sheet-flow experiments in oscillating flow tunnels. For fine sand, this extends to a reversal from offshore- (tunnels) to onshore (flumes)-directed transport. A remarkable hydrodynamic mechanism present in flumes (with free water surface), but not in tunnels (rigid lid), is the generation of progressive wave streaming, an onshore wave boundary layer current. This article investigates whether this streaming is the full explanation of the observed differences in transport. In this article, we present a numerical model of wave-induced sand transport that includes the effects of the free surface on the bottom boundary layer. With these effects and turbulence damping by sediment included, our model yields good reproductions of the vertical profile of the horizontal (mean) velocities, as well as transport rates of both fine and medium sized sediment. Similar to the measurements, the model reveals the reversal of transport direction by free surface effects for fine sand. A numerical investigation of the relative importance of the various free surface effects shows that progressive wave streaming indeed contributes substantially to increased onshore transport rates. However, especially for fine sands, horizontal gradients in sediment advection in the horizontally nonuniform flow field also are found to contribute significantly. We therefore conclude that not only streaming, but also inhomogeneous sediment advection should be considered in formulas of wave-induced sediment transport applied in morphodynamic modeling. We propose a variable time-scale parameter to account for these effects.

Net currents in the wave bottom boundary layer: on waveshape streaming and progressive wave streaming

The net current (streaming) in a turbulent bottom boundary layer under waves above a flat bed, identified as potentially relevant for sediment transport, is mainly determined by two competing mechanisms: an onshore streaming resulting from the horizontal non-uniformity of the velocity field under progressive free surface waves, and an offshore streaming related to the nonlinearity of the waveshape. The latter actually contains two contributions: oscillatory velocities under nonlinear waves are characterized in terms of velocity-skewness and acceleration-skewness (with pure velocity-skewness under Stokes waves and acceleration-skewness under steep sawtooth waves), and both separately induce offshore streaming. This paper describes a 1DV Reynolds-averaged boundary layer model withk-eturbulence closure that includes all these streaming processes. The model is validated against measured period-averaged and time-dependent velocities, from 4 different well-documented laboratory experiments with these processes in isolation and in combination. Subsequently, the model is applied in a numerical study on the waveshape and free surface effects on streaming. The results show how the dimensionless parameterskh (relative water depth) and A/kN (relative bed roughness) influence the (dimensionless) streaming velocity and shear stress and the balance between the mechanisms. For decreasing kh, the relative importance of waveshape streaming over progressive wave streaming increases, qualitatively consistent with earlier analytical modeling. Unlike earlier results, simulations for increased roughness (smaller A/kN) show a shift of the streaming profile in onshore direction for all kh. Finally, the results are parameterized and the possible implications of the streaming processes on sediment transport are shortly discussed

The role of suspended load transport in the occurrence of tidal sand waves

Tidal sand waves are dynamic bed patterns which are formed by the complex interaction between hydrodynamics, sediment transport, and geomorphology. Field data from the southern North Sea reveal that sand waves are absent where suspended load transport is the dominant transport mode. In order to understand the mechanisms responsible for the absence of sand waves, we study the influence of suspended load transport on the formation of tidal sand waves with a numerical process-based geomorphological model (Delft3D). Model simulations are presented in which the vertical eddy viscosity and sediment diffusivity are both spatially and temporally variable (k-e turbulence model). First, it is shown that the preferred wavelength of sand waves for a relatively large grain size increases by the inclusion of suspended sediment, while for a relatively small grain size the flat bed is stable and no sand waves evolve. Second, it is shown that suspended load transport causes the suppression of long sand waves, resulting in a finite range of wavelengths that experience growth. Finally, by varying flow velocity amplitude and grain size, critical conditions for sand wave formation are found, i.e., conditions for which sand waves are marginally generated.

Net currents in the wave boundary layer: balance of wave shape and free surface effects

The net current (streaming) in the bottom boundary layer under waves is mainly determined by two competing mechanisms, namely an offshore streaming related to the non-linearity of the wave shape and an onshore streaming resulting from the horizontal non-uniformity of the velocity field under free surface waves. This paper describes a Reynolds-averaged boundary layer model with k-e turbulence closure that includes both streaming processes. The model is validated on measurements and applied for a numerical study on the balance between the two streaming mechanisms. The results show an increasing importance of the offshore streaming over the onshore streaming for decreasing relative water depth and for decreasing relative bed roughness. Qualitatively, the effect of changing water depth on streaming agrees well with analytical results from literature. We therefore consider the model as a trustworthy framework for future research on the role of wave-induced streaming on sediment transport.