Wheeler Stretching
A limitation of Airy theory is that it only defines wave particle kinematics up to the mean water level (\(z\) = 0). The theory can be extended above the mean water surface, up to the level of the wave crest, by using the Airy formulae with positive values of \(z\). However this approach causes calculation difficulties and is known to over-estimate particle velocities and accelerations in the crest region and to underestimate velocities and accelerations in the troughs. To avoid these difficulties, Bladed uses Wheeler stretching (Wheeler 1970) to take account of the forces acting between mean water level and the instantaneous free surface. Experimental results by (Gudmestad 1993) indicated that Wheeler stretching provides satisfactory estimates of particle kinematics in the free surface zone in deep water.
Wheeler stretching assumes that particle motions calculated using Airy theory at the mean water level should actually be applied at the instantaneous free surface. Airy particle motions calculated at locations between the sea-bed and mean free surface are shifted vertically to new locations in proportion to their height above the sea bed. Airy wave particle kinematics calculated at a vertical location \(z\) are therefore applied to a new location \(\hat{z}\) defined by:
where \(\zeta(t)\) is the surface elevation above the location in question and \(d\) is the mean depth of the water.
Last updated 30-08-2024