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.