Self‐organized kilometer‐scale shoreline sand wave generation: Sensitivity to model and physical parameters

Abstract

The instability mechanisms for self‐organized kilometer‐scale shoreline sand waves have been extensively explored by modeling. However, while the assumed bathymetric perturbation associated with the sand wave controls the feedback between morphology and waves, its effect on the instability onset has not been explored. In addition, no systematic investigation of the effect of the physical parameters has been done yet. Using a linear stability model, we investigate the effect of wave conditions, cross‐shore profile, closure depth, and two perturbation shapes (P1: cross‐shore bathymetric profile shift, and P2: bed level perturbation linearly decreasing offshore). For a P1 perturbation, no instability occurs below an absolute critical angle θc0≈ 40–50°. For a P2 perturbation, there is no absolute critical angle: sand waves can develop also for low‐angle waves. In fact, the bathymetric perturbation shape plays a key role in low‐angle wave instability: such instability only develops if the curvature of the depth contours offshore the breaking zone is larger than the shoreline one. This can occur for the P2 perturbation but not for P1. The analysis of bathymetric data suggests that both curvature configurations could exist in nature. For both perturbation types, large wave angle, small wave period, and large closure depth strongly favor instability. The cross‐shore profile has almost no effect with a P1 perturbation, whereas large surf zone slope and gently sloping shoreface strongly enhance instability under low‐angle waves for a P2 perturbation. Finally, predictive statistical models are set up to identify sites prone to exhibit either a critical angle close to θc0 or low‐angle wave instability.

Rhythmic morphology in a microtidal low-energy beach

“…Thus, we here explore two values, D c = 0.6 m and D c = 0.75 m. Regarding the shape of the bathymetric perturbation a linear decay in bed level from 1 at the shoreline to 0 at D c is considered. The effect of different shape functions on model shoreline sand wave formation is discussed in Idier et al (2017). Regarding the wave conditions we use the SWAN outputs in case of SW breeze as a reference.…”

Formation events of shoreline sand waves on a gravel beach

“…Kaergaard and Fredsoe, 2013a) and on the shape of the bathymetric undulations associated to the shoreline undulations (Idier et al, 2017). In this section we adopt the value θ c = 45 • for being representative of most of the predicted values.…”

“…For this bathymetric perturbation, called P 2, the cross-shore amplitude of the depth contours beyond the surf zone can be larger than the amplitude of the perturbed shoreline (for certain profiles). The influence of this choice in the formation of KSSW has been investigated thoroughly by Idier et al (2017). It was found that low-angle waves can be de-stabilizing only for the perturbation P 2.…”

“…wave instability has been amply confirmed by mathematical modelling during the last two decades. These studies focus on the physics of the basic positive feedback (Ashton et al, 2001;Falqués et al, 2017), the bathymetric and wave conditions which are prone to the instability (Falqués and Calvete, 2005;Idier et al, 2017), its characteristic length scale (van den Berg et al, 2014) and its finite amplitude development (Ashton et al, 2001;Ashton and Murray, 2006a;van den Berg et al, 2012; Kaergaard and Fredsoe, 2013a). Also, the proportion of high-angle waves in the wave climate which is necessary to trigger HAWI has been investigated.…”

Correlation Between Shoreline Change and Planform Curvature on Wave‐Dominated, Sandy Coasts

“…When prevailing waves approach from "low angles" (relative angles less than the flux-maximizing angle), gradients in alongshore transport tend to diverge at convex-seaward (promontory) segments of the shoreline, causing erosion, and converge at concave-seaward (embayed) segments, causing accretion (Ashton et al, 2001;Ashton & Murray, 2006a;Arriaga et al, 2017;Falqués, 2003). Conversely, under a "high angle" wave climate, these gradients in net sediment transport are reversed, such that large-scale coastline curvature tends to increase over time and emergent planform features develop (Ashton et al, 2001;Ashton & Murray, 2006a, 2006bFalqués, 2003;Idier et al, 2017;Murray & Ashton, 2013;van den Berg et al, 2012). In most locations, on some days, the offshore waves approach from high angles relative to the local shoreline orientation, and on some days, they approach from low angles.…”