Linear evolution of sandwave packets

We investigate how a local topographic disturbance of a flat seabed may become morphodynamically active, according to the linear instability mechanism which gives rise to sandwave formation. The seabed evolution follows from a Fourier integral, which can generally not be evaluated in closed form. As numerical integration is rather cumbersome and not transparent, we propose an analytical way to approximate the solution. This method, using properties of the fastest growing mode only, turns out to be quick, insightful, and to perform well. It shows how a local disturbance develops gradually into a sandwave packet, the area of which increases roughly linearly with time. The elevation at the packet¿s center ultimately tends to increase, but this may be preceded by an initial stage of decrease, depending on the spatial extent of the initial disturbance. In the case of tidal asymmetry, the individual sandwaves in the packet migrate at the migration speed of the fastest growing mode, whereas the envelope moves at the group speed. Finally, we apply the theory to trenches and pits and show where results differ from an earlier study in which sandwave dynamics have been ignored

The Stability Balloon for Two-dimensional Vortex Ripple Patterns

Patterns of vortex ripples form when a sand bed is subjected to an oscillatory fluid flow. Here we describe experiments on the response of regular vortex ripple patterns to sudden changes of the driving amplitude a or frequency f. A sufficient decrease of f leads to a "freezing" of the pattern, while a sufficient increase of f leads to a supercritical secondary "pearling" instability. Sufficient changes in the amplitude a lead to subcritical secondary "doubling" and "bulging" instabilities. Our findings are summarized in a "stability balloon" for vortex ripple pattern formation.Comment: 4 pages, 5 figure

Comparing field observations of sorting patterns along tidal sand waves with theoretical predictions

We present a site-by-site comparison between field observations and model predictions of grains size variations over tidal sand waves at six sites in the North Sea. To drive the model, at each location, local sediment characteristics are derived from the described field data, while hydrodynamic conditions are determined from a numerical model for tidal wave propagation in the North Sea. It is found that the theoretical model providesreasonable estimates of the occurring tidally generated bed forms. Moreover, at five of the six locations, the modeldescribes a sorting pattern which concurs with the observed sediment grain size variation, indicating that the model provides a fair description of the processes governing the phenomenon

On the influence of collinear surface waves on turbulence in smooth-bed open-channel flows

This work investigates how turbulence in open-channel flows is altered by the passage of surface waves by using experimental data collected with laboratory tests in a large-scale flume facility, wherein waves followed a current. Flow velocity data were measured with a laser Doppler anemometer and used to compute profiles of mean velocity and Reynolds stresses, and pre-multiplied spectra. The velocity signal containing contributions from the mean flow, wave motion and turbulence was decomposed using the empirical mode decomposition (EMD), which is considered a promising tool for the analysis of velocity time series measured in complex flows. A novel outer length scale h0 is proposed which separates the flow into two regions depending on the competition between the vertical velocities associated with the wave motion and the turbulent velocities imposed by the current. This outer length scale allows for the identification of a genuine overlap layer and an insightful scaling of turbulent statistics in the current-dominated flow region (i.e. y/h0 > 1), a new spectral signature associated with long turbulent structures (approximately 6 and 25 times the flow depth h). As the wave contribution to the vertical velocity increases, the pre-multiplied spectra reveal two intriguing features: (i) in the current-dominated flow region, the very large-scale motions (VLSMs) are progressively weakened but attached eddies are still present; and (ii) in the wave-dominated flow region (i.e. 1$]) appears. These longitudinal structures present in the wave-dominated flow region seem to share many features with Langumir-type cells

Interface-resolved direct numerical simulations of sediment transport in a turbulent oscillatory boundary layer

The flow within an oscillatory boundary layer, which approximates the flow generated by propagating sea waves of small amplitude close to the bottom, is simulated numerically by integrating the Navier-Stokes and continuity equations. The bottom is made up of spherical particles, free to move, which mimic sediment grains. The approach allows one to fully resolve the flow around the particles and to evaluate the forces and torques that the fluid exerts on their surface. Then, the dynamics of sediments is explicitly computed by means of the Newton-Euler equations. For the smallest value of the flow Reynolds number presently simulated, the flow regime turns out to fall in the intermittently turbulent regime such that turbulence appears when the free-stream velocity is close to its largest value but the flow recovers a laminar-like behaviour during the remaining phases of the cycle. For the largest value of the Reynolds number, turbulence is significant during almost the whole flow cycle. The evaluation of the sediment transport rate allows one to estimate the reliability of the empirical predictors commonly used to estimate the amount of sediments transported by sea waves. For large values of the Shields parameter, the sediment flow rate during the accelerating phases does not differ from that observed during the decelerating phases. However, for relatively small values of the Shields parameter, the amount of moving particles depends not only on the bottom shear stress but also on flow acceleration. Moreover, the numerical results provide information on the role that turbulent eddies have on sediment dynamics

Dynamical models for sand ripples beneath surface waves

We introduce order parameter models for describing the dynamics of sand ripple patterns under oscillatory flow. A crucial ingredient of these models is the mass transport between adjacent ripples, which we obtain from detailed numerical simulations for a range of ripple sizes. Using this mass transport function, our models predict the existence of a stable band of wavenumbers limited by secondary instabilities. Small ripples coarsen in our models and this process leads to a sharply selected final wavenumber, in agreement with experimental observations.Comment: 9 pages. Shortened version of previous submissio

A particle model of rolling grain ripples under waves

A simple model is presented for the formation of rolling grain ripples on a flat sand bed by the oscillatory flow generated by a surface wave. An equation of motion is derived for the individual ripples, seen as "particles", on the otherwise flat bed. The model account for the initial apperance of the ripples, the subsequent coarsening of the ripples and the final equilibrium state. The model is related to physical parameters of the problem, and an analytical approximation for the equilibrium spacing of the ripples is developed. It is found that the spacing between the ripples scale with the square-root of the non-dimensional shear stress (the Shields parameter) on a flat bed. The results of the model are compared with measurements, and reasonable agreement between the model and the measurements is demonstrated.Comment: 9 pages incl. figures. Revised versio

Observations of bedforms on a dissipative macrotidal beach

NERC NE/H004262/1 and NE/H02543X/1 DRIB

Stability analysis of ecomorphodynamic equations

In order to shed light on the influence of riverbed vegetation on river morphodynamics, we perform a linear stability analysis on a minimal model of vegetation dynamics coupled with classical one- and two-dimensional Saint-Venant-Exner equations of morphodynamics. Vegetation is modeled as a density field of rigid, nonsubmerged cylinders and affects flow via a roughness change. Furthermore, vegetation is assumed to develop following a logistic dependence and may be uprooted by flow. First, we perform the stability analysis of the reduced one-dimensional framework. As a result of the competitive interaction between vegetation growth and removal through uprooting, we find a domain in the parameter space where originally straight rivers are unstable toward periodic longitudinal patterns. For realistic values of the sediment transport parameter, the dominant longitudinal wavelength is determined by the parameters of the vegetation model. Bed topography is found to adjust to the spatial pattern fixed by vegetation. Subsequently, the stability analysis is repeated for the two-dimensional framework, where the system may evolve toward alternate or multiple bars. On a fixed bed, we find instability toward alternate bars due to flow-vegetation interaction, but no multiple bars. Both alternate and multiple bars are present on a movable, vegetated bed. Finally, we find that the addition of vegetation to a previously unvegetated riverbed favors instability toward alternate bars and thus the development of a single course rather than braiding