Wind-induced changes to shoaling surface gravity wave shape

Unforced shoaling waves experience growth and changes to wave shape. Similarly, wind-forced on a flat-bottom likewise growth/decay However, the combined effect of wind-forcing shape, particularly relevant in near-shore environment, has not yet been investigated theoretically. Here, we consider small-amplitude, shallow-water solitary propagating up gentle, planar bathymetry forced by weak, Jeffreys-type wind-induced surface pressure. We derive variable-coefficient Korteweg-de Vries-Burgers (vKdV-B) equation governing profile's evolution solve it numerically using Runge-Kutta third-order finite difference solver. The simulations run until convective prebreaking -- Froude number limit appropriate order vKdV-B equation. Offshore winds weakly enhance ratio height depth as well slope. Onshore have strong impact narrowing peak, wind also modulates rear shelf formed behind wave. Furthermore, strongly affects width zone, with larger effects for smaller beach slopes. After converting our pressure magnitudes physically realistic speeds, observe qualitative agreement prior laboratory numerical experiments breakpoint location. Additionally, results qualitatively similar temporal shape observations, suggesting that captures essential aspects Finally, isolate wind's comparing profiles unforced case. This reveals are approximately superposition wave, shoaling-induced shelf, wind-induced, bound, dispersive, decaying tail.