# 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

## Notes

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

## Related articles

Shallow-water wave theory