Wave propagation

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Definition of Wave propagation:
Progression and transformation of waves in time and space.
This is the common definition for Wave propagation, other definitions can be discussed in the article


  • The speed [math]c[/math] of a wave propagating without frictional losses in deep water is given by the celerity [math]c \approx \sqrt{g/k} = g/\omega[/math] where [math]g[/math] is the gravitational acceleration, [math]k=2 \pi / \lambda[/math] the wave number, [math]\lambda[/math] the wavelength and [math]\omega=kc[/math] the angular frequency. Deep water means: still water depth [math]h[/math] much larger than [math]1/k[/math]. The dependency of the propagation speed on frequency causes wave dispersion.
  • In shallow water (depth [math]h[/math] much smaller than [math]1/k[/math]), the wave celerity is proportional to the square root of the water depth [math]h[/math] (formula: [math]c \approx \sqrt{gh}[/math]), thus not depending on the wave frequency.
  • In shallow water, wave propagation is a strongly nonlinear process, leading to wave transformation and breaking.
  • A wave group propagates at a smaller speed [math]c_g[/math] than the constituent short waves. Wave energy propagates at the speed of the wave group.

Related articles

Shallow-water wave theory