Abstract
Shoreline undulations extending into the bathymetric contours with a length scale larger than that of the rhythmic surf zone bars are referred to as shoreline sand waves. Many observed undulations along sandy coasts display a wavelength in the order 1-7 km. Several models that are based on the hypothesis that sand waves emerge from a morphodynamic instability in case of very oblique wave incidence predict this range of wavelengths. Here we investigate the physical reasons for the wavelength selection and the main parametric trends of the wavelength in case of sand waves arising from such instability. It is shown that the existence of a minimum wavelength depends on an interplay between three factors affecting littoral drift: (A) the angle of wave fronts relative to local shoreline, which tends to cause maximum transport at the downdrift flank of the sand wave, (B) the refractive energy spreading which tends to cause maximum transport at the updrift flank and (C) wave focusing (de-focusing) by the capes (bays), which tends to cause maximum transport at the crest or slightly downdrift of it. Processes A and C cause decay of the sand waves while process B causes their growth. For low incidence angles, B is very weak so that a rectilinear shoreline is stable. For large angles and long sand waves, B is dominant and causes the growth of sand waves. For large angles and short sand waves C is dominant and the sand waves decay. Thus, wavelength selection depends on process C, which essentially depends on shoreline curvature. The growth rate of very long sand waves is weak because the alongshore gradients in sediment transport decrease with the wavelength. This is why there is an optimum or dominant wavelength. It is found that sand wave wavelength scales with λ0/β where λ0 is the water wave wavelength in deep water and β is the mean bed slope from shore to the wave base.
Highlights
Shoreline sand waves are undulations of the shoreline that extend into the bathymetry up to a certain depth
Some of them are linked to surfzone rhythmic bars but we will here focus on those that are not necessarily linked to surfzone bars and that in general occur at larger length and time scales, i.e., km's and yr's. These shoreline sand waves are episodically or persistently found along many sandy coasts (Bruun 1954, Verhagen, 1989, Inman et al 1992, Thevenot and Kraus 1995, Gravens 1999, Guillén et al 1999, Stive et al 2002, Ruessink and Jeuken 2002, Davidson-Arnott and van Heyningen 2003, Medellín et al 2008, Alves 2009, Vila-Concejo et al 2009, Falqués et al 2011a, Kaergaard et al 2011, Ryabchuk et al 2011). They can be triggered by different physical mechanisms, including forcing by offshore bathymetric anomalies or input of large quantities of sand at inlets and rivers, but they can emerge from irregularities of an otherwise rectilinear coast in absence of any forcing at their length scale
This can occur if the wave climate is dominated by high-angle waves, i.e., waves with a high incidence angle relative to the shore normal, because the rectilinear coast becomes unstable (Ashton et al 2001, Ashton et al 2006a, Falqués et al 2011b) and we will hereinafter refer to them as free or self-organized sand waves
Summary
Shoreline sand waves are undulations of the shoreline that extend into the bathymetry up to a certain depth. Falqués and Calvete (2005) showed that the absence of wavelength selection occurred because the model of Ashton et al (2001) did not take the curvature of bathymetric contours into account If this is accounted for into the wave transformation from deep water up to breaking, there is a cut-off wavelength Lc below which sand waves do not grow and an initially dominant wavelength LM emerges. This wavelength selection was first obtained with linear stability models (Falqués and Calvete 2005, Uguccioni et al 2006) but has recently been confirmed with a nonlinear morphodynamic model (van den Berg et al 2012a).
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