Albert Falqués

A mechanism for the generation of wave-driven rhythmic patterns in the surf zone

The coupling between topographic irregularities and wave-driven mean water motion in the surf zone is examined. This coupling occurs because the topographic perturbations produce excess gradients in the wave radiation stress that cause a steady circulation. This circulation, in turn, creates a sediment transport pattern that can reinforce the bottom disturbance and may thereby lead to the growth of large-scale bed forms. To investigate this coupling mechanism, the linearized stability problem with an originally plane sloping beach and normal wave incidence is solved in two different cases. First, the breaking line is considered to be fixed, and second, the perturbations in water depth that produce a displacement of the breaker line are accounted for. The first case shows that the basic topography can be unstable with respect to two different modes: a giant cusp pattern with shore-attached transverse bars that extend across the whole surf zone and a crescentic pattern with alternate shoals and pools at both sides of the breaking line showing a mirroring effect. In the second case, the varying breaker line may have a strong influence on the circulation. This is clear for the giant cusp topography whose growth is totally inhibited. In contrast, the morphology and the growth of the crescentic pattern remains almost unchanged.

Morphological development of rip channel systems: Normal and near-normal wave incidence

The process of formation of a rip channel/crescentic bar system on a straight, sandy coast is examined. A short review of earlier studies is presented. A morphodynamic stability model is then formulated. The resulting model includes a comprehensive treatment of shoaling and surf zone hydrodynamics, including wave refraction on depth and currents and waves. The sediment transport is modeled using a total load formula. This model is used to study the formation of rip currents and channels on a straight single-barred coast. It is found that this more comprehensive treatment of the dynamics reveals the basic rip cells predicted in earlier studies for normal incidence. Also as before, cell spacings (λ) scale with shore-to-bar crest distance (X b ), while growth rates decrease. The λ increases with offshore wave height (H) up to a saturation value; increasing H also increases instability. Experiments at off-normal wave incidence ( > 0) introduce obliquity into the evolving bed forms, as expected, and λ increases approximately linearly. the e-folding times also increase with . At normal incidence, λ increases weakly with wave period, but at oblique angles, λ decreases. Tests also reveal the presence of forced circulation cells nearer to the shoreline, which carve out bed forms there. The dynamics of these forced cells is illustrated and discussed along with the associated shoreline perturbation. Transverse bars are also discovered. Their dynamics are discussed. Model predictions are also compared with field observations. The relevance of the present approach to predictions of fully developed beach states is also discussed.

Large‐scale dynamics of sandy coastlines: Diffusivity and instability

The dynamics of small-amplitude perturbations of an otherwise rectilinear coastline due to the wave-driven alongshore sediment transport is examined at large time and length scales (years and kilometers). A linear stability analysis is performed by using an extended one-line shoreline model with two main improvements: (1) the curvature of the coastline features is accounted for and (2) the coastline features are assumed to extend offshore as a bathymetric perturbation up to a finite distance. For high incidence angles, instability is found in accordance with Ashton et al. (2001). However, it is seen that instability is inhibited by high waves with long periods and gently sloping shorefaces so that in this case the coastline may be stable for any angle. Similarly, there is no instability if the bathymetric perturbation is confined very close to the coast. It is found that the traditional linearized one-line model (Larson et al., 1987) tends to overpredict the coastline diffusivity. The overprediction is small for the conditions leading to a stable coastline and for moderate incidence angles but can be very dramatic for the conditions favoring instability. An interesting finding is that high-angle waves instability has a dominant wavelength at the linear regime, which is in the order of 4–15 km, one to two orders of magnitude larger than the length scale of surf zone rhythmic features. Intriguingly, this is roughly the same range of the wavelength of some observed shoreline sand waves and, in particular, those observed along the Dutch coast. A model application to this coast is presented.

Modelling the formation and the long‐term behavior of rip channel systems from the deformation of a longshore bar

A nonlinear numerical model based on a wave- and depth-averaged shallow water equation solver with wave driver, sediment transport, and bed updating is used to investigate the long-term evolution of rip channel systems appearing from the deformation of a longshore bar. Linear and nonlinear regimes in the morphological evolution have been studied. In the linear regime, a crescentic bar system emerges as a free instability. In the nonlinear regime, merging/splitting in bars and saturation of the growth are obtained. In spite of excluding undertow and wave-asymmetry sediment transport, the initial crescentic bar system reorganizes to form a large-scale and shore-attached transverse or oblique bar system, which is found to be a dynamical equilibrium state of the beach system. Thus the basic morphological transitions “Longshore Bar and Trough” → “Rhythmic Bar and Beach” → “Transverse Bar and Rip” described by earlier conceptual models are here reproduced. The study of the physical mechanisms allows us to understand the role of the different transport modes: The advective part induces the formation of crescentic bars and megacusps, and the bedslope transport damps the instability. Both terms contribute to the attachment of the megacusps to the crescentic bars. Depending on the wave forcing, the bar wavelength ranges between 180 and 250 m (165 and 320 m) in the linear (nonlinear) regime.

Self-organization mechanisms for the formation on nearshore crescentic and transverse sand bars

The formation and development of transverse and crescentic sand bars in the coastal marine environment has been investigated by means of a nonlinear numerical model based on the shallow-water equations and on a simplified sediment transport parameterization. By assuming normally approaching waves and a saturated surf zone, rhythmic patterns develop from a planar slope where random perturbations of small amplitude have been superimposed. Two types of bedforms appear: one is a crescentic bar pattern centred around the breakpoint and the other, herein modelled for the first time, is a transverse bar pattern. The feedback mechanism related to the formation and development of the patterns can be explained by coupling the water and sediment conservation equations. Basically, the waves stir up the sediment and keep it in suspension with a certain cross-shore distribution of depth-averaged concentration. Then, a current flowing with (against) the gradient of sediment concentration produces erosion (deposition). It is shown that inside the surf zone, these currents may occur due to the wave refraction and to the redistribution of wave breaking produced by the growing bedforms. Numerical simulations have been performed in order to understand the sensitivity of the pattern formation to the parameterization and to relate the hydro-morphodynamic input conditions to which of the patterns develops. It is suggested that crescentic bar growth would be favoured by high-energy conditions and fine sediment while transverse bars would grow for milder waves and coarser sediment. In intermediate conditions mixed patterns may occur.

Generation and nonlinear evolution of shore-oblique/transverse sand bars

The coupling between topography, waves and currents in the surf zone may self-organize to produce the formation of shore-transverse or shore-oblique sand bars on an otherwise alongshore uniform beach. In the absence of shore-parallel bars, this has been shown by previous studies of linear stability analysis, but is now extended to the finite-amplitude regime. To this end, a nonlinear model coupling wave transformation and breaking, a shallow-water equations solver, sediment transport and bed updating is developed. The sediment flux consists of a stirring factor multiplied by the depth-averaged current plus a downslope correction. It is found that the cross-shore profile of the ratio of stirring factor to water depth together with the wave incidence angle primarily determine the shape and the type of bars, either transverse or oblique to the shore. In the latter case, they can open an acute angle against the current (up-current oriented) or with the current (down-current oriented). At the initial stages of development, both the intensity of the instability which is responsible for the formation of the bars and the damping due to downslope transport grow at a similar rate with bar amplitude, the former being somewhat stronger. As bars keep on growing, their finite-amplitude shape either enhances downslope transport or weakens the instability mechanism so that an equilibrium between both opposing tendencies occurs, leading to a final saturated amplitude. The overall shape of the saturated bars in plan view is similar to that of the small-amplitude ones. However, the final spacings may be up to a factor of 2 larger and final celerities can also be about a factor of 2 smaller or larger. In the case of alongshore migrating bars, the asymmetry of the longshore sections, the lee being steeper than the stoss, is well reproduced. Complex dynamics with merging and splitting of individual bars sometimes occur. Finally, in the case of shore-normal incidence the rip currents in the troughs between the bars are jet-like while the onshore return flow is wider and weaker as is observed in nature.

Bed.flow instability of the longshore current

Abstract An initially uniform longshore current on a plane erodible beach is considered and a linear stability analysis of the bed-flow system is performed in order to investigate the growth of alongshore periodic topographic features such as transverse or oblique bars. γ, numerical model based on the shallow water equations and a simple sediment transport formula is used. For a wide range of parameters instability is found, leading to the growth of large-scale topographic features (lengthscale of the order of the current width) downflow progressing. The growth rates and the dominant unstable mode depend mainly on R = cd/β parameter, where cd is the bottom friction coefficient and β is the beach slope. For a small R, say less than 0.1, instability is very weak, probably negligible. For R between 0.1 and 0.7 instability increases with R, leading typically to a quite simple transverse bars pattern. A further increase in R produces a far more complicated behaviour where complex patterns with downcurrent oriented oblique bars, bumps and holes can be dominant. In this region growth rates may either decrease or increase with R depending on the beach slope and the maximum Froude number of the basic flow, F. Usually, the most complex behaviour is found for gently sloping beaches. The physical mechanism of the instability is found to lie on the disturbances of potential vorticity caused by topographically induced differences in bottom friction. In this sense it is similar to the alternate bars growth in a river rather than the dunes or antidunes occurrence for 1D channel flow. The predictions of the model compare well with the available experimental data. The alongshore wavelength, γ, typically of the order of one to four times the width of the current, is close to four times for the most common values of R. The typical growth time is proportional to γ2 and for a wavelength of 100 m can be of the order of one day, depending on the sediment transport rate. The migrational speed is inversely proportional to γ, in accordance to earlier field data reported by Sonu (1969) Collective movement of sediment in littoral environment.

Modelling the formation of shoreface-connected sand ridges on storm-dominated inner shelves

A morphodynamic model is developed and analysed to gain fundamental understanding of the basic physical mechanisms responsible for the characteristics of shorefaceconnected sand ridges observed in some coastal seas. These alongshore rhythmic bed forms have a horizontal lengthscale of order 5 km and are related to the mean current along the coast: the seaward ends of their crests are shifted upstream with respect to where they are attached to the shoreface. The model is based on the two-dimensional shallow water equations and assumes that the sediment transport only takes place during storms. The flux consists of a suspended-load part and a bed-load part and accounts for the e ects of spatially non-uniform wave stirring as well as for the preferred downslope movement of sediment. The basic state of this model represents a steady longshore current, driven by wind and a pressure gradient. The dynamics of small perturbations to this state are controlled by a physical mechanism which is related to the transverse bottom slope. This causes a seaward deflection of the current over the ridges and the loss of sediment carrying capacity of the flow into deeper water. The orientation, spacing and shape of the modelled ridges agree well with eld observations. Suspended-load transport and spatially non-uniform wave stirring are necessary in order to obtain correct e-folding timescales and migration speeds. The ridge growth is only due to suspended-load transport whereas the migration is controlled by bed-load transport.

Some spectral approximations for differential equations in unbounded domains

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Numerical simulation of vorticity waves in the nearshore

A numerical method based on spectral expansions is given for the computation of vorticity waves arising from shear instability of a longshore current. This method allows for any mean flow profile and any beach topography (remaining constant alongshore and with a straight shoreline). The shallow-water equations are considered without any assumption about the sea surface (such as rigid lid), and dissipative terms accounting for bottom friction and/or eddy viscosity are included. A numerical simulation for some flow profiles that are quite realistic in the surf zone and for several bathymetries is presented. For inviscid flow the predictions of the Bowen and Holman (1989) analytical model for a very simplified geometry are found to give rise to the main features. However, the details in the flow and depth profiles are found to significantly influence the instability curves, especially for a barred beach. For the fastest growing mode, the wavelength is between 1.7 and 2.7 times the width of the mean current l. Frequencies of about 0.09ƒs, where ƒs is the maximum shear at the sea face of the current profile, and an e-folding time of the exponential growth that is roughly equal to the wave period are obtained. The phase speed is between 0.5 and 0.7 of the mean current peak. Dissipation has a considerable effect on the wavenumber span and the growth rate of the instability, so reasonably constant values of the eddy viscosity and realistic values of the Chezy coefficient can entirely remove the instability. The phase speed of neutral shear waves is analytically found to be equal to the mean flow velocity at the cross-shore location where the potential vorticity has an extremum. This velocity is found to give an estimate of the phase speed of growing modes. We found that the rigid-lid assumption tends to overestimate the growth rates by an amount which depends on the maximum Froude number of the mean flow. The instability curves and the dispersion lines for a free surface converge towards the rigid-lid ones when the Froude number decreases, and the rigid-lid assumption is therefore valid for a low Froude number.