A morphodynamic model based on the wave-driven alongshore sediment transport, including crossshor... more A morphodynamic model based on the wave-driven alongshore sediment transport, including crossshore transport in a simplified way and neglecting tides, is presented and applied to the Zandmotor meganourishment on the Dutch Delfland coast. The model is calibrated with the bathymetric data surveyed from January 2012 to March 2013 using measured offshore wave forcing. The calibrated model reproduces accurately the surveyed evolution of the shoreline and depth contours until March 2015. According to the long-term modeling using different wave climate scenarios based on historical data, for the next 30-yr period, the Zandmotor will display diffusive behavior, asymmetric feeding to the adjacent beaches, and slow migration to the NE. Specifically, the Zandmotor amplitude will have decayed from 960 m to about 350 m with a scatter of only about 40 m associated to climate variability. The modeled coastline diffusivity during the 3-yr period is 0.0021 m 2 /s, close to the observed value of 0.0022 m 2 /s. In contrast, the coefficient of the classical one-line diffusion equation is 0.0052 m 2 /s. Thus, the lifetime prediction, here defined as the time needed to reduce the initial amplitude by a factor 5, would be 90 yr instead of the classical diffusivity prediction of 35 yr. The resulting asymmetric feeding to adjacent beaches produces 100 m seaward shift at the NE section and 80 m seaward shift at the SW section. Looking at the variability associated to the different wave climates, the migration rate and the slight shape asymmetry correlate with the wave power asymmetry (W vs N waves) while the coastline diffusivity correlates with the proportion of high-angle waves, suggesting that the Dutch coast is near the high-angle wave instability threshold.
X-2 FERNÁNDEZ-MORA ET AL.: ONSHORE SANDBAR MIGRATION We present a novel process-based morphodynam... more X-2 FERNÁNDEZ-MORA ET AL.: ONSHORE SANDBAR MIGRATION We present a novel process-based morphodynamic model, which includes transport processes due to both velocity and acceleration skewness and a new formulation for intra-wave motions, that successfully simulates observed of onshore sandbar migration. Results confirm findings of previous studies, in which each process was considered separately and in which sediment transport was computed from the observed water motion. However, our results indicate that accounting for the joint action of both velocity and acceleration skewnesses causes major improvement of the modeled onshore bar migration, and is essential to accurately model the evolution of the entire crossshore bottom profile, when compared with observations. We also demonstrate that the morphodynamics in the shoaling zone are dominated by velocity skewness (bed-shear stresses), while sediment transport induced by acceleration skewness (pressure gradients) controls the morphodynamics in the inner surf zone.
A theoretical analysis of the effect of a longshore mean shear flow on edge waves is performed in... more A theoretical analysis of the effect of a longshore mean shear flow on edge waves is performed in the framework of linear shallow water equations. A single equation describing edge waves as well as neutral shear waves is obtained. A numerical method of calculation is given for the dispersion relations and the wave pattern, accounting for any beach topography and any mean flow profile (remaining constant alongshore and with a straight shoreline). Numerical calculations are presented for a simple exponential flow profile and for a plane bottom. A Doppler shift in the frequencies and a variation in the offshore extension of the waves are found, depending on the maximum local Froude number of the current, F, defined as F = [V(x)/ dm],,,, where V(X) stands for the mean longshore current, H(x) for the depth, and g for the gravity. The maximum shift in frequency is for wave numbers of about V,(O)'/gm and frequencies of about V,(O), where V,(O) is the shear at the shoreline and m is the beach slope. For instance, these maximum differences may reach about 40% for F=O.5. Waves of any wavelength can always propagate downstream, but they can propagate upstream only for F < F,-0.7'. For mean flows with F> F, only waves shorter or longer than some forbidden wavelengths can propagate against the current. An analytical dispersion relation of asymptotic general validity for short waves (corresponding to the gravity range in real beaches) is given. The numerical model as well as this analytical dispersion relation is tested by means of a nonplanar real topography.
The steady perturbation caused in a longshore flow by a bottom undulation is considered. The bedf... more The steady perturbation caused in a longshore flow by a bottom undulation is considered. The bedforms are assumed to be alongshore periodic, with crests in the cross-shore direction and with a small amplitude in order for linear theory to be applicable. The inviscid shallow-water equations are considered in order to investigate topographic resonance, that is, the condition under which the perturbation in the flow reaches a maximum. Since upstream edge waves held stationary by the mean flow are solutions to the homogeneous resonance equations, the existence of such flows gives rise to the existence of resonances of infinite amplitude (linear, inviscid theory). For a maximum local Froude number of the basic flow F of less than 1, the flow is found to behave subcritically according to classic channel flow theory. In addition, neither steady edge waves nor infinite amplitude resonances exist in this case. However, by numerical simulation, a finite maximum in the how perturbation as a function of bedform wavelength is found. This topographic resonance is rather weak and wide banded. For a bedform height of 1% the local water depth, the perturbation on the flow may typically be 4% of the mean current. The resonant wavelength is between two and three times the distance of the peak longshore current to the shoreline, IV, when the current profile has a maximum at some distance offshore, or nearly four times the cross-shore length scale of the sandbars, 1, for a flow profile monotonically increasing to a constant current far offshore. For F > I resonances of infinite amplitude are found. For every F, I,, and Z, there is an infinite set of resonant modes with an increasing cross-shore complexity when the mode number increases, similarly to edge waves. The resonant wavelength increases with F and with I,. Some implications on the growth of transverse sandbar families and cuspidal coast are discussed.
mAn initially uniform longshore current on a plane erodible beach is considered and a linear stab... more mAn 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. A 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 = cdl fl parameter, where c d is the bottom friction coefficient and fl 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, 2, 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 it 2 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 2, in accordance to earlier field data reported by Sonu [(1969) Collective movement of sediment in littoral environment.
Nearshore sandbars are often characterized by three-dimensional bed patterns. To analyze the infl... more Nearshore sandbars are often characterized by three-dimensional bed patterns. To analyze the influence of wave direction on the morphological response of a double sandbar system, this paper uses the 2DH nonlinear surf zone model MORFO55. Depending on wave direction, different morphologies emerge as free instabilities. These morphological responses differ in terms of geometry (shape of the alongshore rhythmic patterns) and temporal evolution. Nearly shore-normal waves favor the emergence of crescentic patterns along both the inner and outer bars. These instabilities arise from ''bedsurf'' coupling, which is the positive feedback between the bed perturbations and the wave-breaking patterns resulting in rip-cell circulations. The system is stable for intermediate wave incidence angles because the longshore current shifts the circulation cells alongshore, inhibiting the growth of initial perturbations. For larger angles, the system is again unstable. Two types of oblique bars emerge. The first type forms between the crest of the inner bar and the shoreline and is oriented down-current. The second type is superimposed on the two bars and is oriented up-current. Although previous studies attribute the formation of oblique bars to the deflection of the longshore current (that is a cross-shore process), we show here that this mechanism contributes to the bar formation but the growth rate is mainly governed by a longshore process. Specifically, it is the positive feedback between the bathymetry and the longshore gradient of the sediment concentration. Finally, interactions between the patterns in the two shore-parallel bars are analyzed. In the observed configurations, the influence is always one way as the inner-bar dynamics never influence those of the outer bar. The outer-bar instabilities cause undulations in the inner bar when the outer-bar instabilities grow faster than those of the inner bar.
Work undertaken in the EU HUMOR project on morphodynamical modelling, particularly with regard to... more Work undertaken in the EU HUMOR project on morphodynamical modelling, particularly with regard to simulating and understanding rhythmic surf zone bars and related morphodynamic self-organization, is presented. These features are reviewed and their engineering context stated. Hydrodynamical and morphodynamical models developed and/or applied within the HUMOR project in order to address these issues are briefly presented. The linear stability modelling concept and stability studies using fully nonlinear models are contrasted. The stability of a shoreparallel bar under normal or oblique wave incidence is chosen as a test case for the different models. The results are compared and discussed. Lastly, modelling efforts and main results from the project are summarized. Recommendations for further work are made.
A numerical method based on spectral expansions is given for the computation of vorticity waves a... more 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 0.09oe•, where oe• 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 rigidlid ones when the Froude number decreases, and the rigid-lid assumption is therefore valid for a low Froude number.
Shoreline instability caused by very oblique wave incidence should develop only at very large len... more Shoreline instability caused by very oblique wave incidence should develop only at very large length and time scales on open ocean beaches. For this reason a direct observation of this instability is difficult. On sheltered steep beaches those scales can however be considerably smaller. We here analyze video observations of shoreline position along El Puntal Spit in Santander (Spain) for a two-month event where shoreline sand waves form, evolve and finally disappear. We then test whether the observed sand waves could be governed by high angle waves instability. Preliminary results show a quite good overall correspondence between observations and instability model, in particular, regarding the wavelength (~125m). However, the model predicts downdrift propagation while the sand wave does not appreciably propagate.
Método de reducción al contorno método de reducción al contorno con superficie libre
La descripción usual del movimiento de un fluido incompresible en régimen potencial, bajo la acci... more La descripción usual del movimiento de un fluido incompresible en régimen potencial, bajo la acción de la gravedad, con su superficie superior libre, viene dada por la ecuación de Laplace -lineal y sin derivadas respecto al tiempo- y unas condiciones de contorno en la superficie libre que generan toda la dependencia temporal y las no-linealidades. En este artículo se presenta una formulación del problema en términos -exclusivamente- de las variables restringidas a la superficie libre. Esta formulación presenta varias ventajas, tanto desde un punto de vista teórico como práctico. Algunas de ellas son puestas de manifiesto mediante el ejemplo de aplicación que presentamos: el cálculo numérico de las frecuencias de resonancia de un recinto con una variación brusca de profundidad
The aim of the present study is to analyse the mid-term beach profile evolution, considering the ... more The aim of the present study is to analyse the mid-term beach profile evolution, considering the hypothesis that the alongshore processes can be neglected for the prediction of the mean profile evolution. To this end, a processbased model for the evolution of the cross-shore profile has been used. The model describes feedbacks between waves, rollers, depth-averaged currents and bed evolution, accounting for the effects of wave skewness and asymmetry on sediment transport. Offshore waves and tides conditions and bathymetric profiles measured at the FRF-USACE Duck are used to simulate a mid-term (72 days) onshore sandbar migration event. The model results agree with observed onshore movement and growth of the sandbar due to the inclusion of the intra-wave oscillatory flow with the skewness and asymmetry effects. The best predictions belongs to the averaging of the modelled evolution of individual cross-shore profiles that is better than the evolution of the mean cross-shore profile since.it takes into account the alongshore variability of the cross-shore profiles. These two methods result on better predictions than the individual profiles during the entire event.
Contour-line models as tools for long-term coastal evolution
INTRODUCTION In engineering applications, the two most widely used model types up till now, for c... more INTRODUCTION In engineering applications, the two most widely used model types up till now, for coastal evolution analyses, have been the one-line model and the profile change model. In one-line models the changes in shoreline position are assumed to be produced by spatial and temporal differences in the longshore sand transport rate (Hanson 1989, Hanson et al. 1988). This type of model is used to calculate shoreline changes that occur over a period of years to decades. Cross-shore transport effects, such as storm-induced erosion and cyclical movement of shoreline position associated with seasonal variation in wave climate, are assumed to cancel over a long enough simulation period or are accounted for through external calculations.
Breaker bars in the surf zone of sandy beaches generally evolve between straight bars parallel to... more Breaker bars in the surf zone of sandy beaches generally evolve between straight bars parallel to the shore and meandering crescentic bars associated with intense (dangerous) currents flowing seaward through rip channels. Understanding the behavior of such systems is fundamental as they control the entire surf zone dynamics, the shape of the coastline, and the exchange of floating material with the shoreface. Although the mechanisms behind the meandering of an originally straight bar have been studied extensively, a clear physical explanation on the crescentic bar straightening was missing. Recent field observations have highlighted that this morphological reset can be due to wave obliquity. By using a two-dimensional horizontal morphological model, we show that the bar straightening by oblique waves occurs because the rip current is both weakened in intensity and shifted downdrift from the channel deepest section. The technique employed is useful for the study of other types of bed forms.
Sandy coasts sometimes develop a variety of complicated morphological patterns that in some cases... more Sandy coasts sometimes develop a variety of complicated morphological patterns that in some cases are characterized by a striking spatial periodicity along the coast. Crescentic sand bars provide an intriguing example of such rhythmic patterns. These features develop in the surf zone, are shaped as crescent moons parallel the coast. They have been observed to exhibit alongshore wavelengths ranging between
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