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.Postprint (published version

Frontshear and backshear instabilities of the mean longshore current

An analytical model based on Bowen and Holman [1989] is used to prove the existence of instabilities due to the presence of a second extremum of the background vorticity at the front side of the longshore current. The growth rate of the so-called frontshear waves depends primarily upon the frontshear but also upon the backshear and the maximum and the width of the current. Depending on the values of these parameters, either the frontshear or the backshear instabilities may dominate. Both types of waves have a cross-shore extension of the order of the width of the current, but the frontshear modes are localized closer to the coast than are the backshear modes. Moreover, under certain conditions both unstable waves have similar growth rates with close wave numbers and angular frequencies, leading to the possibility of having modulated shear waves in the alongshore direction. Numerical analysis performed on realistic current profiles confirm the behavior anticipated by the analytical model. The theory has been applied to a current profile fitted to data measured during the 1980 Nearshore Sediment Transport Studies experiment at Leadbetter Beach that has an extremum of background vorticity at the front side of the current. In this case and in agreement with field observations, the model predicts instability, whereas the theory based only on backshear instability fai led to do so

Reply to comment by M. Ortega-Sánchez et al. on “High-angle wave instability and emergent shoreline shapes : 1. Modeling of sand waves, flying spits, and capes”

Author Posting. © American Geophysical Union, 2008. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Journal of Geophysical Research 113 (2008): F01006, doi:10.1029/2007JF000885

Formas cuspidales de playas y procesos de la zona de rompientes interna: ¿crecimiento o destrucción? Aplicación a la playa de Trafalgar (Cádiz, España)

Large beach cusps (LBC, wavelength of ~ 30 m) are intertidal features that can alternately exist in the swash and in the inner surf zone due to tidal sea level changes. They have a larger cross-shore extent (up to 50 m) than traditional cusps. This extent has been explained by a shift of the swash zone during falling tide. The cusps immerse at rising tide and previous studies indicate that surf zone processes are exclusively destructive. Here, the behaviour of large beach cusps in the inner surf zone is investigated by using a 2DH morphological numerical model applied to Trafalgar Beach (Cádiz, Spain). The model results indicate that the inner surf zone processes do not always destroy the cusps but can in fact reinforce them by considering neither the swash processes nor the tidal changes. More generally, in conditions favouring the presence of the LBC the surf zone of a beach can be unstable, leading to the formation of transverse/oblique sand bars that can have characteristics similar to the LBC. Thus, in principle, the LBC could emerge not only due to swash zone morphodynamics but also due to surf zone morphodynamics or a combination of both.Las formas cuspidales de grandes dimensiones (LBC, longitudes de onda ~30 m) constituyen un sistema morfológico rítmico a lo largo de la playa que tiene una parte que se encuentra alternativamente en la zona de swash (flujo/reflujo) y en la zona de rompientes interna debido a los cambios del nivel del mar. Tienen una distancia de penetración de hasta 50 m, superior por tanto a la de las cúspides ordinarias. Esta elongación parece debido a la traslación de la zona de swash durante la marea descendente. En marea ascendente estas estructuras están sumergidas y los estudios previos consideran que los procesos de la zona de rompientes las destruyen. En este trabajo se analiza el comportamiento de estas formas en la zona de rompientes de la playa de Trafalgar (Cádiz) usando un modelo numérico morfológico 2DH. Los resultados muestran que, sin considerar ni los procesos de swash ni el cambio de marea, los procesos de la zona de rompientes no necesariamente destruyen LBC, sino que pueden reforzarlas. De forma más general, en condiciones favorables a la presencia de LBC, se pueden formar barras de arena con características similares a LBC debido a procesos de auto-organización en la zona de rompientes.The work of R. Garnier was supported by the University of Nottingham and is part of the Spanish Government project under contract CTM2006-08875. The Spanish Ministry of Science and Education (Project BORRASCAS CTM2005-06583) and the Junta de Andalucía (Projects P05-RNM-968 and P06-RNM-1573) funded part of this research

High-angle wave instability and emergent shoreline shapes : 1. Modeling of sand waves, flying spits, and capes

Author Posting. © American Geophysical Union, 2006. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Journal of Geophysical Research 111 (2006): F04011, doi:10.1029/2005JF000422.Contrary to traditional findings, the deepwater angle of wave approach strongly affects plan view coastal evolution, giving rise to an antidiffusional “high wave angle” instability for sufficiently oblique deepwater waves (with angles between wave crests and the shoreline trend larger than the value that maximizes alongshore sediment transport, ∼45°). A one-contour-line numerical model shows that a predominance of high-angle waves can cause a shoreline to self-organize into regular, quasiperiodic shapes similar to those found along many natural coasts at scales ranging from kilometers to hundreds of kilometers. The numerical model has been updated from a previous version to include a formulation for the widening of an overly thin barrier by the process of barrier overwash, which is assumed to maintain a minimum barrier width. Systematic analysis shows that the wave climate determines the form of coastal response. For nearly symmetric wave climates (small net alongshore sediment transport), cuspate coasts develop that exhibit increasing relative cross-shore amplitude and pointier tips as the proportion of high-angle waves is increased. For asymmetrical wave climates, shoreline features migrate in the downdrift direction, either as subtle alongshore sand waves or as offshore-extending “flying spits,” depending on the proportion of high-angle waves. Numerical analyses further show that the rate that the alongshore scale of model features increases through merging follows a diffusional temporal scale over several orders of magnitude, a rate that is insensitive to the proportion of high-angle waves. The proportion of high-angle waves determines the offshore versus alongshore aspect ratio of self-organized shoreline undulations.This research was funded by the Andrew W. Mellon Foundation and NSF grants DEB-05-07987 and EAR-04-44792

Understanding coastal morphodynamic patterns from depth-averaged sediment concentration

This review highlights the important role of the depth-averaged sediment concentration (DASC) to understand the formation of a number of coastal morphodynamic features that have an alongshore rhythmic pattern: beach cusps, surf zone transverse and crescentic bars, and shoreface-connected sand ridges. We present a formulation and methodology, based on the knowledge of the DASC (which equals the sediment load divided by the water depth), that has been successfully used to understand the characteristics of these features. These sand bodies, relevant for coastal engineering and other disciplines, are located in different parts of the coastal zone and are characterized by different spatial and temporal scales, but the same technique can be used to understand them. Since the sand bodies occur in the presence of depth-averaged currents, the sediment transport approximately equals a sediment load times the current. Moreover, it is assumed that waves essentially mobilize the sediment, and the current increases this mobilization and advects the sediment. In such conditions, knowing the spatial distribution of the DASC and the depth-averaged currents induced by the forcing (waves, wind, and pressure gradients) over the patterns allows inferring the convergence/divergence of sediment transport. Deposition (erosion) occurs where the current flows from areas of high to low (low to high) values of DASC. The formulation and methodology are especially useful to understand the positive feedback mechanisms between flow and morphology leading to the formation of those morphological features, but the physical mechanisms for their migration, their finite-amplitude behavior and their decay can also be explored

Role of the forcing sources in morphodynamic modelling of an embayed beach

The sensitivity of a 2DH coastal area (XBeach) and a reduced-complexity (Q2Dmorfo) morphodynamic model to using different forcing sources is studied. The models are tested by simulating the morphodynamic response of an embayed beach in the NW Mediterranean over a 6-month period. Wave and sea-level forcing from in situ data, propagated buoy measurements, and hindcasts, as well as combinations of these different data sources, are used, and the outputs are compared to in situ bathymetric measurements. Results show that when the two models are calibrated with in situ measurements, they accurately reproduce the morphodynamic evolution with a “good” Brier skill score (BSS). The calibration process reduces the errors by 65 %–85 % compared with the default setting. The wave data propagated from the buoy also produce reliable morphodynamic simulations but with a slight decrease in the BSS. Conversely, when the models are forced with hindcast wave data, the mismatch between the modelled and observed beach evolution increases. This is attributed to a large extent to biased mean directions in hindcast waves. Interestingly, in this small tide site, the accuracy of the simulations hardly depends on the sea-level data source, and using filtered or non-filtered tides also yields similar results. These results have implications for long-term morphodynamic studies, like those needed to validate models for climate change projections, emphasizing the need to use accurate forcing sources such as those obtained by propagating buoy data.</p

High-angle wave instability and emergent shoreline shapes : 2. Wave climate analysis and comparisons to nature

Author Posting. © American Geophysical Union, 2006. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Journal of Geophysical Research 111 (2006): F04012, doi:10.1029/2005JF000423.Recent research has revealed that the plan view evolution of a coast due to gradients in alongshore sediment transport is highly dependant upon the angles at which waves approach the shore, giving rise to an instability in shoreline shape that can generate different types of naturally occurring coastal landforms, including capes, flying spits, and alongshore sand waves. This instability merely requires that alongshore sediment flux is maximized for a given deepwater wave angle, a maximum that occurs between 35° and 50° for several common alongshore sediment transport formulae. Here we introduce metrics that sum over records of wave data to quantify the long-term stability of wave climates and to investigate how wave climates change along a coast. For Long Point, a flying spit on the north shore of Lake Erie, Canada, wave climate metrics suggest that unstable waves have shaped the spit and, furthermore, that smaller-scale alongshore sand waves occur along the spit at the same locations where the wave climate becomes unstable. A shoreline aligned along the trend of the Carolina Capes, United States, would be dominated by high-angle waves; numerical simulations driven by a comparable wave climate develop a similarly shaped cuspate coast. Local wave climates along these simulated capes and the Carolina Capes show similar trends: Shoreline reorientation and shadowing from neighboring capes causes most of the coast to experience locally stable wave climates despite regional instability.This research was funded by the Andrew W. Mellon Foundation and NSF grants DEB-05-07987 and EAR-04-44792