Related papers: New gravity-capillary waves at low speeds. Part 2:…
In 1982, Marshall P. Tulin published a report proposing a framework for reducing the equations for gravity waves generated by moving bodies into a single nonlinear differential equation solvable in closed form [Proc. 14th Symp. on Naval…
We construct small-amplitude solitary traveling gravity-capillary water waves with a finite number of point vortices along a vertical line, on finite depth. This is done using a local bifurcation argument. The properties of the resulting…
It was recently found that, when linearised in the absence of matter, 58 cases of the general gravitational theory with quadratic curvature and torsion are (i) free from ghosts and tachyons and (ii) power-counting renormalisable. We inspect…
The higher-order Stokes phenomenon can emerge in the asymptotic analysis of many problems governed by singular perturbations. Indeed, over the last two decades, the phenomena has appeared in many physical applications, from acoustic and…
We establish the existence of gravity water waves by applying a mountain pass theorem to a singular perturbation of the Alt-Caffarelli functional associated with the two-dimensional water wave equations. Our approach is formulated entirely…
We consider the Rayleigh-Taylor problem for two compressible, immiscible, inviscid, barotropic fluids evolving with a free interface in the presence of a uniform gravitational field. After constructing Rayleigh-Taylor steady-state solutions…
The surface gravity wave pattern that forms behind a steadily moving disturbance is well known to comprise divergent waves and transverse waves, contained within a distinctive V-shaped wake. In this paper, we are concerned with a…
A nonlinear theory of pattern selection in parametric surface waves (Faraday waves) is presented that is not restricted to small viscous dissipation. By using a multiple scale asymptotic expansion near threshold, a standing wave amplitude…
We prove the existence and the linear stability of small amplitude time {\it quasi-periodic} standing wave solutions (i.e. periodic and even in the space variable $ x $) of a $ 2 $-dimensional ocean with infinite depth under the action of…
In general relativity (GR), linearized gravitational waves propagating in empty Minkowski spacetime along a fixed spatial direction have the property that the wave front is the Euclidean plane. Beyond the linear regime, exact plane waves in…
Gravitational waves in the presence of a non-minimal curvature-matter coupling are analysed, both in the Newman-Penrose and perturbation theory formalisms. Considering a cosmological constant as a source, the non-minimally coupled…
We study the two-dimensional gravity-capillary water waves equations for a fluid of finite depth $\mathtt{h}>0$ under the combined effects of gravity and surface tension $\kappa \geq 0$. We analyze the linear stability and instability of…
We discuss the propagation of gravitational waves in a recently discussed class of theories containing N >= 2 metric tensors and a corresponding number of standard model copies. Using the formalism of gauge-invariant linear perturbation…
In some modified theories of gravity, gravitational waves can contain up to six different polarizations, which can travel at speeds different from that of light. Searches for these different polarizations in gravitational wave data are…
We present a theoretical study of nonlinear pattern formation in parametric surface waves for fluids of low viscosity, and in the limit of large aspect ratio. The analysis is based on a quasi-potential approximation to the equations…
In the low-speed limit, a blunt ship modeled as two-dimensional semi-infinite body with a single corner can never be made waveless. This was the conclusion of the previous part of our work in Trinh et al. (2011), which focused on the Dagan…
We present a numerical study of spatially quasi-periodic gravity-capillary waves of finite depth in both the initial value problem and traveling wave settings. We adopt a quasi-periodic conformal mapping formulation of the Euler equations,…
We investigate the vacuum pp-wave and Aichelburg-Sexl-type solutions in f(R) and the modified Gauss-Bonnet theories of gravity with both minimal and nonminimal couplings between matter and geometry. In each case, we obtain the necessary…
We consider a layer of an inviscid fluid with free surface which is subject to vertical high-frequency vibrations. We derive three asymptotic systems of equations that describe slowly evolving (in comparison with the vibration frequency)…
The coupled motion is investigated for a mechanical system consisting of water and a body freely floating in it. Water occupies either a half-space or a layer of constant depth into which an infinitely long surface-piercing cylinder is…