# Shoaling

 Definition of Shoaling: Shoaling is the deformation of incident waves on the lower shoreface that starts when the water depth becomes less than about half of the wavelength, causing the waves to become steeper: increase in amplitude and decrease in wavelength. This is the common definition for Shoaling, other definitions can be discussed in the article

## Notes

• Wave amplification is due to (approximate) continuity of the wave energy flux $F=c_g E$ seaward of the surf zone, where $E = \frac{1}{8} \rho g H^2$ is the wave energy and $c_g$ the wave group propagation speed. The landward decrease of the wave group propagation speed ($c_g \approx \sqrt{gh}$ in shallow water of depth $h$) results in a landward increase of $E$, thus in a landward increase of wave height $H$. See: Shallow-water wave theory for a more detailed treatment.
• Wave propagation in the shoaling zone has a strongly non-linear character because the wave height is no longer negligible compared to the water depth. This produces wave asymmetry, with the wave orbital velocity being greater in the onshore than offshore direction and the offshore-to-onshore orbital acceleration being greater than the onshore-to-offshore acceleration.
• Wave shoaling precedes wave breaking on the upper shoreface when the wave steepness exceeds a critical limit.

Shoaling wave.