Shoaling
From Coastal Wiki
|
Definition of Wave shoaling:
The transformation of surface gravity waves as they propagate into shallower water, involving changes in wave height, wavelength and wave shape. Wave height generally increases, wavelength decreases, and nonlinear effects can cause wave crests to become sharper and wave fronts to steepen.
This is the common definition for Wave shoaling, other definitions can be discussed in the article
|
Notes
- Wave height amplification is due to the approximate conservation of wave energy flux [math]F=c_g E[/math] when wave energy dissipation is negligible. In linear wave theory, [math]E = \frac{1}{8} \rho g H^2[/math] is the wave energy per unit horizontal area, [math]H[/math] the wave height, [math]c_g[/math] the wave group velocity (energy propagation speed), [math]g[/math] the gravitational acceleration and [math]\rho[/math] the water density. As waves propagate into shallower water, the group velocity eventually decreases ([math]c_g \approx \sqrt{gh}[/math] in shallow water of depth [math]h[/math]). Conservation of energy flux then requires an increase in wave energy density and hence in wave height. In shallow water, Green's law gives [math]H \propto h^{-1/4}[/math]. See Shallow-water wave theory for a more detailed treatment.
- Wave propagation becomes strongly nonlinear when the water depth is small compared with the wavelength and the wave height is not negligible compared with the water depth. Shoaling under these conditions is often accompanied by wave deformation, including sharper crests and steepening of the wave front. Nonlinear wave deformation also produces asymmetric orbital velocities and accelerations, with stronger onshore than offshore orbital velocities and stronger offshore-to-onshore than onshore-to-offshore accelerations (see Shoreface profile).
- Shoaling can eventually lead to wave breaking when the wave becomes unstable, for example when the wave height becomes too large relative to the local water depth (see Breaker index).
