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S. L. Woodruff

Bio: S. L. Woodruff is an academic researcher from University of Michigan. The author has contributed to research in topics: Gravitational wave & Capillary wave. The author has an hindex of 1, co-authored 1 publications receiving 12 citations.

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Journal ArticleDOI
TL;DR: In this article, a simple and effective multiscale approach for nonlinear asymptotic short-wave dynamics in dispersive systems is devised for wave dynamics and perturbative methods, which allows for a general classification of classical model equations as Boussinesq, Benjamin-Bona-Mahony-Peregrine and Camassa-Holm equations.
Abstract: Nonlinear monochromatic short surface waves in ideal fluids are studied and, by the general consideration of wave dynamics and perturbative methods a simple and effective multiscale approach is devised for nonlinear asymptotic short-wave dynamics in dispersive systems. In particular the evolution of a monochromatic surface wave in an ideal fluid is shown to lead to a modified Green-Naghdi system of equations and a Green-Naghdi system with surface tension. Short surface waves exist in these systems and the nonlinear asymptotic analysis produces the nonlinear model equations that govern their dynamics. Particular solutions are shown. Moreover the method allows for a general classification of classical model equations as Boussinesq, Benjamin-Bona-Mahony-Peregrine and Camassa-Holm equations. Their related nonlinear short-wave model limits are then derived. A relation between the short-wave limit of the integrable Camassa-Holm equation and the Harry-Dym hierarchy is finally unveiled.

24 citations

Journal ArticleDOI
TL;DR: In this paper, a nonlinear equation governing asymptotic dynamics of monochromatic short surface wind waves is derived by using a short wave perturbative expansion on a generalized version of the Green-Naghdi system.

22 citations

Journal ArticleDOI
TL;DR: Parasitic ripple generation on short gravity waves (4 cm to 10 cm wavelengths) was examined using fully nonlinear computations and laboratory experiments in this article, where the maximum ripple steepness (in time) was found to increase monotonically with the underlying (lowfrequency bandpass) wave steepness.
Abstract: Parasitic ripple generation on short gravity waves (4 cm to 10 cm wavelengths) is examined using fully nonlinear computations and laboratory experiments. Timemarching simulations show sensitivity of the ripple steepness to initial conditions, in particular to the crest asymmetry. Signicant crest fore{aft asymmetry and its unsteadiness enhance ripple generation at moderate wave steepness, e.g. ka between 0.15 and 0.20, a mechanism not discussed in previous studies. The maximum ripple steepness (in time) is found to increase monotonically with the underlying (lowfrequency bandpass) wave steepness in our simulations. This is dierent from the subor super-critical ripple generation predicted by Longuet-Higgins (1995). Unsteadiness in the underlying gravity{capillary waves is shown to cause ripple modulation and an interesting ‘crest-shifting’ phenomenon { the gravity{capillary wave crest and the rst ripple on the forward slope merge to form a new crest. Including boundary layer eects in the free-surface conditions extends some of the simulations at large wave amplitudes. However, the essential process of parasitic ripple generation is nonlinear interaction in an inviscid flow. Mechanically generated gravity{capillary waves demonstrate similar characteristic features of ripple generation and a strong correlation between ripple steepness and crest asymmetry.

14 citations

Journal ArticleDOI
TL;DR: In this article, a theoretical and experimental study of the propagation of a short gravity wave packet (modulated Stokes wave) over a solitary wave was performed using a WKB-type perturbation method.
Abstract: This paper is a theoretical and experimental study of the propagation of a short gravity wave packet (modulated Stokes wave) over a solitary wave. The theoretical approach used here relies on a nonlinear WKB-type perturbation method. This method yields a theory of gravity waves that can describe both short and long waves simultaneously. We obtain explicit analytical solutions describing the interaction between the soliton and the short wave packet: phase shifts, variations of wavelengths and of frequencies (Doppler effects). In the experimental part of this work the phase shift experienced by the Stokes wave is measured. The theoretical conclusions are confirmed.

13 citations

Journal ArticleDOI
TL;DR: In this article, a new nonlinear equation governing asymptotic dynamics of short surface waves is derived by using a short-wave perturbative expansion in an appropriate reduction of the Euler equations.
Abstract: A new nonlinear equation governing asymptotic dynamics of short surface waves is derived by using a short-wave perturbative expansion in an appropriate reduction of the Euler equations. This reduction corresponds to a Green-Naghdi-type equation with a cinematic discontinuity in the surface. The physical system under consideration is an ideal fluid (inviscid, incompressible and without surface tension) in which takes place a steady surface motion. An ideal surface wind on a lake which produces surface flow is a physical environment conducive to the above-mentioned phenomenon. The equation obtained admits peakon solutions with amplitude, velocity and width in interrelation.

12 citations