Water waves

Source: Wikipedia. Pages: 85. Chapters: Flood, Tsunami, Gravity wave, Wake, Cnoidal wave, Airy wave theory, Storm surge, Rogue wave, List of floods, Dispersion, Mild-slope equation, Megatsunami, List of rogue waves, Radiation stress, Wind wave, Stokes drift, Tsunamis in lakes, Boussinesq approximation, Seiche, Capillary wave, Clapotis, Flash flood, Equatorial waves, Wind wave model, Wave radar, Morison equation, Breaking wave, Shallow water equations, Wave shoaling, Internal wave, Wave making resistance, Wave turbulence, Ocean dynamics, Significant wave height, Infragravity wave, Surf break, Hull speed, Extratropical storm surge, Ursell number, Swell, Keulegan-Carpenter number, Hundred-year wave, Sneaker wave, Wave-current interaction, Meteotsunami, Douglas Sea Scale, List of waves named after people, Undertow, 1934 Muroto typhoon, Draupner wave, Bow wave, Wave base, Edge wave, Artificial wave, Cross sea, Waves and shallow water, Wave-piercing, Coriolis-Stokes force. Excerpt: In fluid dynamics, a cnoidal wave is a nonlinear and exact periodic wave solution of the Korteweg-de Vries equation. These solutions are in terms of the Jacobi elliptic function cn, which is why they are coined cnoidal waves. They are used to describe surface gravity waves of fairly long wavelength, as compared to the water depth. The cnoidal wave solutions were derived by Korteweg and de Vries, in their 1895 paper in which they also propose their dispersive long-wave equation, now known as the Korteweg-de Vries equation. In the limit of infinite wavelength, the cnoidal wave becomes a solitary wave. The Benjamin-Bona-Mahony equation has improved short-wavelength behaviour, as compared to the Korteweg-de Vries equation, and is another uni-directional wave equation with cnoidal wave solutions. Further, since the Korteweg-de Vries equation is an approximation to the Boussinesq equations for the case of one-way wave propagation, cnoidal waves are approximate solutions to the Boussinesq equations. Cnoidal wave solutions can appear in other applications than surface gravity waves as well, for instance to describe ion acoustic waves in plasma physics. Validity of several theories for periodic water waves, according to Le Méhauté (1976). The light-blue area gives the range of validity of cnoidal wave theory; light-yellow for Airy wave theory; and the dashed blue lines demarcate between the required order in Stokes' wave theory. The light-gray shading gives the range extension by numerical approximations using fifth-order stream-function theory, for high waves (H > ¿ Hbreaking).The Korteweg-de Vries equation (KdV equation) can be used to describe the uni-directional propagation of weakly nonlinear and long waves-where long wave means: having long wavelengths as compared with the mean water depth-of surface gravity waves on a fluid layer. The KdV equation is a dispersive wave equation, including both frequency dispersion and amplitude dispersion effects. In its classical u