Can edge waves be generated by wind?

Abstract

Edge waves, the infragravity waves trapped by near-shore topography, are important in morphodynamics and flooding on mildly sloping beaches. Edge waves are usually generated by swell via triad interactions. Here, we examine the possibility that edge waves might be also generated directly by wind. By processing data from the SandyDuck’97 near-shore experiment, we show that pronounced directional asymmetry of edge waves does occur in nature, apparently unrelated to the direction of swells and along-shore currents. These observations exhibit edge waves propagating in the downwind direction under moderate wind against the along-shore currents, while swell is incident nearly normally to the shoreline, which strongly suggests generation of edge waves by wind. We examine theoretically possible mechanisms of edge-wave excitation by wind. We show that the ‘maser’ mechanism suggested by Longuet-Higgins (Proc. R. Soc. Lond. A, vol. 311, issue 1506, 1969b, pp. 371–389) in the context of excitation of free water waves is effective under favourable conditions: nonlinearly interacting random short wind-forced waves create a viscous shear stress on the water surface with the variation of stress being phase linked to edge waves, which allows self-excitation of a coherent edge wave. The model we put forward is based upon the kinetic equation for short wind waves propagating on the inhomogeneous current due to an edge wave. The model needs a dedicated experiment for validation. Analysis of plausible alternative mechanisms of generation via Miles’ critical layer and via the viscous shear stresses induced by the edge wave in the air revealed no instability in the consideration confined to the main mode and constant slope bathymetry.

Unsteady edge waves generated by time-harmonic pressure: exact solutions

“…It is a time-harmonic function depending on two functions of spatial coordinates. But in contrast to the works [10,15], in the presented paper an exact solution of complete hydrodynamic equations for edge waves in an ideal fluid was obtained. Note that it also describes unsteady waves with vorticity.…”

“…Thus, instead of three initial equations, two equations can be solved only, e.g. ( 14) and (15). Formally, they coincide with the equations of two-dimensional hydrodynamics, where the variable q plays the role of the Cartesian Lagrangian coordinate b.…”

“…Shrira et al, based on the data of the SandyDuck'97 nearshore experiment [14], came to the conclusion that edge waves can be generated by the wind [15]. They showed that the 'maser' mechanism proposed by Longuet-Higgins [16] in the context of excitation of free water waves is effective under favorable conditions, when interacting nonlinearly random short wind-forced waves create a viscous shear stress at the water surface with the variation of stress phase linked to the edge waves.…”