When waves travel into areas of shallow water, they begin to be affected by the ocean bottom. The free orbital motion of the water is disrupted, and water particles in orbital motion no longer return to their original position. As the water becomes shallower, the swell becomes higher and steeper, ultimately assuming the familiar sharp-crested wave shape. After the wave breaks, it becomes a wave of translation and erosion of the ocean bottom intensifies.
Cnoidal waves are exact periodic solutions to the Korteweg–de Vries equation in shallow water, that is, when the wavelength of the wave is much greater than the depth of the water.
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The course is an introduction to symmetry analysis in fluid mechanics. The student will learn how to find similarity and travelling-wave solutions to partial differential equations used in fluid and c
Related concepts (3)
Explores shallow water waves, stability conditions, and tsunamis through simulations and analytical solutions.
Explores waves in inhomogeneous media, covering initial and boundary conditions, numerical stability, eigen modes, and propagation principles.
Discusses the linearization of shallow water wave equations and the impact of variable depth on wave propagation velocity.
In fluid dynamics, the Boussinesq approximation for water waves is an approximation valid for weakly non-linear and fairly long waves. The approximation is named after Joseph Boussinesq, who first derived them in response to the observation by John Scott Russell of the wave of translation (also known as solitary wave or soliton). The 1872 paper of Boussinesq introduces the equations now known as the Boussinesq equations. The Boussinesq approximation for water waves takes into account the vertical structure of the horizontal and vertical flow velocity.
In fluid dynamics, dispersion of water waves generally refers to frequency dispersion, which means that waves of different wavelengths travel at different phase speeds. Water waves, in this context, are waves propagating on the water surface, with gravity and surface tension as the restoring forces. As a result, water with a free surface is generally considered to be a dispersive medium. For a certain water depth, surface gravity waves – i.e.
In fluid dynamics, a wind wave, or wind-generated water wave, is a surface wave that occurs on the free surface of bodies of water as a result of the wind blowing over the water's surface. The contact distance in the direction of the wind is known as the fetch. Waves in the oceans can travel thousands of kilometers before reaching land. Wind waves on Earth range in size from small ripples to waves over high, being limited by wind speed, duration, fetch, and water depth.
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Within the frame of the Third Rhône Correction, the river bend in Martigny is considered a top priority measure for flood protection. During the preliminary project, physical and numerical modeling tests were considered necessary. For the latter, the softw ...
International Research Society INTERPRAEVENT2021
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The study of non-contact manipulation in water, and the ability to robotically control floating objects has gained recent attention due to wide-ranging potential applications, including the analysis of plastic pollution in the oceans and the optimization o ...
This paper proposes high-order accurate well-balanced (WB) energy stable (ES) adaptive moving mesh finite difference schemes for the shallow water equations (SWEs) with non flat bottom topography. To enable the construction of the ES schemes on moving mesh ...