Search results
Results from the WOW.Com Content Network
In 2002, the regularized version of the KP equation, naturally referred to as the Benjamin–Bona–Mahony–Kadomtsev–Petviashvili equation (or simply the BBM-KP equation), was introduced as an alternative model for small amplitude long waves in shallow water moving mainly in the x direction in 2+1 space.
Boussinesq approximation (water waves) – Approximation valid for weakly non-linear and fairly long waves; Mild-slope equation – Physics phenomenon and formula; Shallow water equations – Set of partial differential equations that describe the flow below a pressure surface in a fluid; Stokes drift – Average velocity of a fluid parcel in a ...
The wave equation is a second-order linear partial differential equation for the description of waves or standing wave fields such as mechanical waves (e.g. water waves, sound waves and seismic waves) or electromagnetic waves (including light waves). It arises in fields like acoustics, electromagnetism, and fluid dynamics.
In deep water, longer period waves propagate faster and transport their energy faster. The deep-water group velocity is half the phase velocity. In shallow water, for wavelengths larger than twenty times the water depth, [14] as found quite often near the coast, the group velocity is equal to the phase velocity.
Intuitively the wave envelope is the "global profile" of the wave, which "contains" changing "local profiles inside the global profile". Each propagates at generally different speeds determined by the important function called the dispersion relation.
Cnoidal wave solution to the Korteweg–De Vries equation, in terms of the square of the Jacobi elliptic function cn (and with value of the parameter m = 0.9). Numerical solution of the KdV equation u t + uu x + δ 2 u xxx = 0 (δ = 0.022) with an initial condition u(x, 0) = cos(πx). Time evolution was done by the Zabusky–Kruskal scheme. [1]
Shallow-water equations can be used to model Rossby and Kelvin waves in the atmosphere, rivers, lakes and oceans as well as gravity waves in a smaller domain (e.g. surface waves in a bath). In order for shallow-water equations to be valid, the wavelength of the phenomenon they are supposed to model has to be much larger than the depth of the ...
Another variation of the moving hydraulic jump is the cascade. In the cascade, a series of roll waves or undulating waves of water moves downstream overtaking a shallower downstream flow of water. A moving hydraulic jump is called a surge. The travel of wave is faster in the upper portion than in the lower portion in case of positive surges