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We derive here a new stability criterion for two-fluid interfaces. This criterion ensures the existence of "stable" local solutions that do no break down too fast due to Kelvin-Helmholtz instabilities. It can be seen both as a two-fluid…
This paper considers two-dimensional stably stratified steady periodic gravity water waves with surface profiles monotonic between crests and troughs. We provide sufficient conditions under which such waves are necessarily symmetric. This…
The problem of determining the threshold of motion of a sediment particle resting on the bed of an open channel has historically been dominated by an approach based on the time-space-averaged bed shear stress (i.e. Shields criterion).…
The interaction of obliquely incident surface gravity waves with a vertical flexible permeable membrane wave barrier is investigated in the context of three-dimensional linear wave-structure interaction theory. A general formulation for…
We consider the 2D gravity water waves equation on an infinite domain. We prove a local wellposedness result which allows interfaces with corners and cusps as initial data and which is such that the time of existence of solutions is uniform…
It is well-known that the Camassa-Holm (CH) equation admits both of the peaked and cusped solitary waves in shallow water. However, it was an open question whether or not the exact wave equations can admit them in finite water depth.…
Swimming is ubiquitous in nature and crucial for the survival of a wide range of organisms. The physics of swimming at the viscosity-dominated microscale and inertia-dominated macroscale is well studied. However, in between lies a…
This paper is concerned with the wave breaking phenomena for a coupled periodic Camassa-Holm system. We establish a new blowup criterion for strong solutions by the method of characteristic and convolution estimates, and also give the…
The data analysis problem of coherently searching for unmodeled gravitational-wave bursts in the data generated by a global network of gravitational-wave observatories has been at the center of research for almost two decades. As data from…
A family of Camassa-Holm type equations with a linear term and cubic and quartic nonlinearities is considered. Local well-posedness results are established via Kato's approach. Conserved quantities for the equation are determined and from…
Wave breaking is an important process for energy dissipation in the open ocean and coastal seas. It drives beach morphodynamics, controls air-sea interactions, determines when ship and offshore structure operations can occur safely, and…
Observations show that maximally-steep breaking water wave crest speeds are much slower than expected. We report a wave-crest slowdown mechanism generic to unsteady propagating deep water wave groups. Our fully nonlinear computations show…
Gravitational wave burst is a catch-all category for signals whose durations are shorter than the observation period. We apply a method new to gravitational wave data analysis --- Bayesian non-parameterics --- to the problem of…
We consider the two dimensional gravity water wave equation in the regime that includes free surfaces with angled crests. We assume that the fluid is inviscid, incompressible and irrotational, the air density is zero, and we neglect the…
Dam breach models are commonly used to predict outflow hydrographs of potentially failing dams and are key ingredients for evaluating flood risk. In this paper a new dam breach modeling framework is introduced that shall improve the…
A typical approach to developing an analysis algorithm for analyzing gravitational wave data is to assume a particular waveform and use its characteristics to formulate a detection criteria. Once a detection has been made, the algorithm…
The gravity water waves equations describe the evolution of the surface of an incompressible, irrotational fluid in the presence of gravity. The classical regularity threshold for the well-posedness of this system requires initial velocity…
In the framework of the canonical model of hydrodynamics, where fluid is assumed to be ideal and incompressible, waves are potential, two-dimensional, and symmetric, the authors have recently reported the existence of a new type of gravity…
Accurate mapping of ocean bathymetry is a multi-faceted process, needed for safe and efficient navigation on shipping routes and for predicting tsunami waves. Currently available bathymetry data does not always provide the resolution to…
We present a comprehensive theory for linear gravity-driven ship waves in the presence of a shear current with uniform vorticity, including the effects of finite water depth. The wave resistance in the presence of shear current is…