Wave propagation
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
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Notes
- The speed [math]\displaystyle{ c }[/math] of a wave propagating without frictional losses in deep water is given by the celerity [math]\displaystyle{ c \approx \sqrt{g/k} = g/\omega }[/math] where [math]\displaystyle{ g }[/math] is the gravitational acceleration, [math]\displaystyle{ k=2 \pi / \lambda }[/math] the wave number, [math]\displaystyle{ \lambda }[/math] the wavelength and [math]\displaystyle{ \omega=kc }[/math] the angular frequency. Deep water means: still water depth [math]\displaystyle{ h }[/math] much larger than [math]\displaystyle{ 1/k }[/math]. The dependency of the propagation speed on frequency causes wave dispersion.
- In shallow water (depth [math]\displaystyle{ h }[/math] much smaller than [math]\displaystyle{ 1/k }[/math]), the wave celerity is proportional to the square root of the water depth [math]\displaystyle{ h }[/math] (formula: [math]\displaystyle{ 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]\displaystyle{ c_g }[/math] than the constituent short waves. Wave energy propagates at the speed of the wave group.