Difference between revisions of "Wave propagation"
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==Notes== | ==Notes== | ||
| − | *The speed <math>c</math> of a wave propagating without frictional losses in deep water is given by <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 [[Dispersion (waves)|wave dispersion]]. | + | *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 [[Dispersion (waves)|wave dispersion]]. |
| − | *In shallow water (depth <math>h</math> much smaller than <math>1/k</math>), the wave | + | *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. | *In shallow water, wave propagation is a strongly nonlinear process, leading to wave transformation and breaking. | ||
*A [[Wave group|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. | *A [[Wave group|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. | ||
Latest revision as of 10:14, 4 March 2022
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]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.
