Water wave propagation and scattering over topographical bottoms

Here I present a general formulation of water wave propagation and scattering over topographical bottoms. A simple equation is found and is compared with existing theories. As an application, the theory is extended to the case of water waves in a column with many cylindrical steps

Comparison between three-dimensional linear and nonlinear tsunami generation models

The modeling of tsunami generation is an essential phase in understanding tsunamis. For tsunamis generated by underwater earthquakes, it involves the modeling of the sea bottom motion as well as the resulting motion of the water above it. A comparison between various models for three-dimensional water motion, ranging from linear theory to fully nonlinear theory, is performed. It is found that for most events the linear theory is sufficient. However, in some cases, more sophisticated theories are needed. Moreover, it is shown that the passive approach in which the seafloor deformation is simply translated to the ocean surface is not always equivalent to the active approach in which the bottom motion is taken into account, even if the deformation is supposed to be instantaneous.Comment: 39 pages, 16 figures; Accepted to Theoretical and Computational Fluid Dynamics. Several references have been adde

The Basics of Water Waves Theory for Analogue Gravity

This chapter gives an introduction to the connection between the physics of water waves and analogue gravity. Only a basic knowledge of fluid mechanics is assumed as a prerequisite.Comment: 36 pages. Lecture Notes for the IX SIGRAV School on "Analogue Gravity", Como (Italy), May 201

Water waves generated by a moving bottom

Tsunamis are often generated by a moving sea bottom. This paper deals with the case where the tsunami source is an earthquake. The linearized water-wave equations are solved analytically for various sea bottom motions. Numerical results based on the analytical solutions are shown for the free-surface profiles, the horizontal and vertical velocities as well as the bottom pressure.Comment: 41 pages, 13 figures. Accepted for publication in a book: "Tsunami and Nonlinear Waves", Kundu, Anjan (Editor), Springer 2007, Approx. 325 p., 170 illus., Hardcover, ISBN: 978-3-540-71255-8, available: May 200

Matter rogue wave in Bose-Einstein condensates with attractive atomic interaction

We investigate the matter rogue wave in Bose-Einstein Condensates with attractive interatomic interaction analytically and numerically. Our results show that the formation of rogue wave is mainly due to the accumulation of energy and atoms toward to its central part; Rogue wave is unstable and the decay rate of the atomic number can be effectively controlled by modulating the trapping frequency of external potential. The numerical simulation demonstrate that even a small periodic perturbation with small modulation frequency can induce the generation of a near-ideal matter rogue wave. We also give an experimental protocol to observe this phenomenon in Bose-Einstein Condensates

Proceedings Nonlinear Water Waves Workshop, 22-25 October 1991

The aim of this workshop was to take advantage of the recent freedom available to scientists in the Soviet Union (now Commonwealth of Independent States) to travel to the West in order to develop both contacts and an awareness of current research between research workers from East and West, most of whom have formerly had little contact. We consider this aim was achieved and are grateful for the substantial financial support from the European Office of the U.S. Office of Naval Research and the European Research Office of the U.S. Army. In addition we thank the home institutions or other fund providers which supported the travel costs of participants and the subsistence of western participants. The support of Bristol University's Department of Mathematics in holding the meeting is greatly appreciated

Wave Breaking

Water waves break as they advance over a gently sloping beach for all off-shore sea states except for the calmest conditions. Most theoretical, experimental and field studies have been directed to this type of wave breaking, yet waves can break with greater violence on steep slopes and close to coastal structures and cliffs. Further, on those occasions when winds are actively generating waves, the offshore incident wave field already has a significant density of breaking waves before any effects of shoaling or coastal currents stimulate more breaking. It is easy to appreciate why most attention has been given to waves breaking on gently sloping beaches. Comparison with experiments shows that the assumption of slowly-varying properties for a periodic wave train can give a description of wave height variation, which together with a breaking criterion is adequate for many engineering purposes, though the effects of irregular and three-dimensional incident waves are not well documented or analysed. Theoretical treatments for other bathymetry or steep incident waves have only recently become available for research purposes, and the interaction between theory and experiment which is so vital to greater understanding is only just developing. Here, we first discuss the breaking criterion for classical slowly-varying wave theory. Current knowledge on the kinematics and dynamics of wave breaking is then briefly surveyed. Brief comments are given on the effects of subsurface structures and vertical walls on two-dimensional breaking, followed by some thoughts on the problems of sealing from experiments, or numerical models, to prototype.ICCE 199