arXiv subjects

Falk Feddersen

Publications and source records attributed to Falk Feddersen.

3 recordsLinked to original sources

arXiv2022

Wind-Induced Changes to Shoaling Surface Gravity Wave Shape

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

physics.flu-dyn↗

arXiv2021

Wind-Induced Changes to Surface Gravity Wave Shape in Shallow Water

Wave shape (e.g. wave skewness and asymmetry) impacts sediment transport, remote sensing and ship safety. Previous work showed that wind affects wave shape in intermediate and deep water. Here, we investigate the effect of wind on wave shape in shallow water through a wind-induced surface pressure for different wind speeds and directions to provide the first theoretical description of wind-induced shape changes. A multiple-scale analysis of long waves propagating over a shallow, flat bottom and forced by a Jeffreys-type surface pressure yields a forward or backward Korteweg-de Vries (KdV)-Burgers equation for the wave profile, depending on the wind direction. The evolution of a symmetric, solitary-wave initial condition is calculated numerically. The resulting wave grows (decays) for onshore (offshore) wind and becomes asymmetric, with the rear face showing the largest shape changes. The wave profile's deviation from a reference solitary wave is primarily a bound wave and trailing, dispersive, decaying tail. The onshore wind increases the wave's energy and skewness with time while decreasing the wave's asymmetry, with the opposite holding for offshore wind. The corresponding wind speeds are shown to be physically realistic, and the shape changes are explained as slow growth followed by rapid evolution according to the unforced KdV equation.

physics.flu-dyn↗

arXiv2020

Wind-Induced Changes to Surface Gravity Wave Shape in Deep to Intermediate Water

Wave shape (i.e. skewness or asymmetry) plays an important role in beach morphology evolution, remote sensing, and ship safety. Wind's influence on ocean waves has been extensively studied theoretically in the context of growth, but most theories are phase averaged and cannot predict wave shape. Most laboratory and numerical studies similarly focus on wave growth. A few laboratory experiments have demonstrated that wind can change wave shape, and two-phase numerical simulations have also noted wind-induced wave shape changes. However, wind's effect on wave shape is poorly understood, and no theory for it exists. For weakly nonlinear waves, wave shape parameters are the phase of the harmonic relative to the primary frequency (or harmonic phase HP, zero for a Stokes wave) and relative amplitude of the harmonic to the primary. Here, surface pressure profiles (denoted Jeffreys, Miles, and Generalized Miles) are prescribed based on wind-wave generation theories. Theoretical solutions are derived for quasi-periodic progressive waves and the wind-induced changes to HP, relative harmonic amplitude, as well as already known phase speed changes and growth rates. The wave shape parameters depend upon the chosen surface pressure profile, pressure magnitude and phase relative to the wave profile, and the nondimensional depth. Wave asymmetry is linked to the nondimensional growth rate. Atmospheric large eddy simulations constrain pressure profile parameters. HP predictions are qualitatively consistent with laboratory observations. This theory, together with the observables of HP and relative harmonic amplitude, can provide insight into the actual wave surface pressure profile.

physics.flu-dyn↗