A new instability mechanism related to high-angle waves

Abstract

Waves with a large incidence angle in deep water can drive a morphodynamic instability on a sandy coast whereby shoreline sand waves, cuspate forelands, and spits can emerge. This instability is related to bathymetric perturbations extending offshore in the shoaling zone. Here, we explore a different mechanism where the large incidence angle is supposed to occur at breaking and the bathymetric perturbations occur only in the surf zone. For wave incidence angles at breaking above ≈ 45^∘, the one-line approximation of coastal dynamics predicts an unstable shoreline. This instability (EHAWI) is scale-free and the growth rate increases without bound for decreasing wavelength. Here we use a 2DH morphodynamic model resolving surf zone instabilities to investigate whether EHAWI could approximate a real instability in nature with a characteristic length scale. Assuming very idealized conditions on the bathymetric profile and sediment transport, we find a 2DH instability mode consisting of shore-oblique up-current bars coupled to a meandering of the longshore current. This mode grows for high-angle waves, above about 30^∘ (offshore) and the maximum growth rate occurs for the angle maximizing the angle at breaking, about 70^∘ (offshore). The dominant wavelength is of the order of the surf zone width. Interestingly, for long sand waves, the growth rate never becomes negative and it matches very well the anti-diffusive behavior of EHAWI. This distinguishes the present instability mode from other modes found in previous studies for other bathymetric and sediment transport conditions. Thus, we conclude that EHAWI approximates a real morphodynamic instability only for quite particular conditions. In such case, a characteristic length scale of the instability emerges thanks to surf zone processes that damp short wavelengths.