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We review here the derivation of many of the most important models that appear in the literature (mainly in coastal oceanography) for the description of waves in shallow water. We show that these models can be obtained using various…

Analysis of PDEs · Mathematics 2020-04-22 David Lannes

Breaching of earthen or sandy dams/dunes by overtopping flow and waves is a complicated process with strong, unsteady flow, high sediment transport, and rapid bed changes in which the interactions between flow and morphology should not be…

Fluid Dynamics · Physics 2015-08-06 Zhiguo He , Peng Hu , Liang Zhao , Ganfeng Wu , Thomas Pähtz

It is believed that there are extra fundamental gauge symmetries beyond these described by the Standard Model of particle physics. The scale of these new gauge symmetries are usually too high to be reachable by particle colliders.…

High Energy Physics - Phenomenology · Physics 2017-08-01 Wei Chao , Wen-Feng Cui , Huai-Ke Guo , Jing Shu

In this paper we study wave breaking in the unidirectional non-local wave model describing the motion of a collision-free plasma in a magnetic field. By analyzing the monotonicity and continuity properties of a system of the Riccati-type…

Analysis of PDEs · Mathematics 2023-06-14 Shaojie Yang , Jian Chen

We consider the angle $\theta$ of inclination (with respect to the horizontal) of the profile of a steady 2D inviscid symmetric periodic or solitary water wave subject to gravity. Although $\theta$ may surpass 30$^\circ$ for some…

Analysis of PDEs · Mathematics 2016-07-26 Walter A. Strauss , Miles H. Wheeler

Line waves are recently discovered wave entities that are localized along two directions, and therefore can be viewed as the one-dimensional counterpart of surface waves. These waves can be supported at discontinuities of the surface…

We investigate the potential of neural-network based classifiers for discriminating gravitational wave bursts (GWBs) of a given canonical family (e.g. core-collapse supernova waveforms) from typical transient instrumental artifacts…

Instrumentation and Methods for Astrophysics · Physics 2014-01-24 Salvatore Rampone , Vincenzo Pierro , Luigi Troiano , Innocenzo M. Pinto

Following conservative solutions of the nonlinear variational wave equation $u_{tt}-c(u)(c(u)u_x)_x=0$ along forward and backward characteristics, we identify criteria, which guarantee that wave breaking either occurs in the nearby future…

Analysis of PDEs · Mathematics 2025-02-28 Sondre Tesdal Galtung , Katrin Grunert

The detection of GW150914 by ground based gravitational wave observatories has brought about a new era in astrophysics. At optimal sensitivity, these observatories are expected to detect several events each year, with one or two of these…

General Relativity and Quantum Cosmology · Physics 2017-06-14 Nicolas Loutrel , Nicolas Yunes

In high-speed maritime operations, the broaching phenomenon can pose a significant risk when navigating in following/quartering seas. The occurrence of this phenomenon can result in a violent yaw motion, regardless of the steering effort,…

General Mathematics · Mathematics 2024-06-21 Atsuo Maki , Masahiro Sakai , Tetsushi Ueta

Accurate prediction of shallow water flows relies on precise bottom topography data, yet direct bathymetric surveys are expensive and time-consuming. In contrast, remote sensing platforms such as radar or satellite altimetry provide…

Numerical Analysis · Mathematics 2026-03-13 Falko Ruppenthal , Dmitri Kuzmin

We consider the stability of periodic gravity free-surface water waves traveling downstream at a constant speed over a shear flow of finite depth. In case the free surface is flat, a sharp criterion of linear instability is established for…

Analysis of PDEs · Mathematics 2007-11-28 Vera Mikyoung Hur , Zhiwu Lin

We study dispersion properties of linear surface gravity waves propagating in an arbitrary direction atop a current profile of depth-varying magnitude using a piecewise linear approximation, and develop a robust numerical framework for…

Fluid Dynamics · Physics 2017-08-02 Benjamin K. Smeltzer , Simen Å. Ellingsen

In these notes, we comment on the standard indistinguishability criterion often used in the gravitational wave community to set accuracy requirements on waveforms. Revisiting the hypotheses under which it is derived, we propose a correction…

General Relativity and Quantum Cosmology · Physics 2024-01-19 Alexandre Toubiana , Jonathan R. Gair

The performances of phase-averaged parametric nearshore wave transformation models depend significantly on a reliable estimate of the wave breaker index r (the breaker height-to-depth ratio), a free model parameter that essentially controls…

Atmospheric and Oceanic Physics · Physics 2021-06-10 Chi Zhang , Yuan Li , Yu Cai , Jian Shi , Jinhai Zheng , Feng Cai , Hongshuai Qi

A global network of laser interferometric gravitational wave detectors is projected to be in operation by around the turn of the century. Here, the noisy output of a single instrument is examined. A gravitational wave is assumed to have…

General Relativity and Quantum Cosmology · Physics 2009-10-30 David Nicholson , Alberto Vecchio

The statistics of breaking wave fields is characterised within a novel multi-layer framework, which generalises the single-layer Saint-Venant system into a multi-layer and non-hydrostatic formulation of the Navier-Stokes equations. We…

Fluid Dynamics · Physics 2023-08-09 Jiarong Wu , Stéphane Popinet , Luc Deike

A novel mathematical nonlinear theory of surface gravity waves in deep water is presented, in which analytical analysis of the classical nonlinear equations of fluid dynamics is performed under less restrictive assumptions than those…

Fluid Dynamics · Physics 2022-02-24 Ilia Mindlin

In this paper we consider fundamental processes of the disturbance and propagation of internal gravity waves in the ocean modeled as a vertically stratified, horizontally non-uniform, and non-stationary medium. We develop asymptotic methods…

Fluid Dynamics · Physics 2013-08-20 Vitaly V. Bulatov , Yuriy V. Vladimirov

We present a new differential mechanical gradiometer for the detection of low-frequency Gravitational Waves. The frequency range is 0.05 to 1 Hz, a frequency gap not covered either by future space-based detectors such as LISA or by…

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