Page 208 - Dynamic Loading and Design of Structures

Page 181

Figure 5.5 Wave elevation and kinematics; (a) Linear theory; (b) wave crest kinematics.

The horizontal velocity and acceleration are seen to have their absolute maximum values at
crest/trough and wave nodes, respectively. The wave elevation, dynamic pressure and
horizontal velocity are in phase, while the horizontal acceleration is 90° out of phase.
Moreover, it is seen that the kinematics (e.g. horizontal velocity) at locations half a
wavelength apart is in opposite phase. These phase relationships are of considerable
significance for calculation of wave loads on structures (Figure 5.5). Further details about the
Airy theory may be found, for example, in Clauss et

Modifications of the kinematics of linear theory
The linear theory is valid only for small values of wave amplitudes. Particle velocities in the
crest region will especially be subject to significant uncertainties, which will affect drag
forces, which are proportional to velocity squared, and other loads which depend upon crest
kinematics. Rather than extrapolating, for example, the particle velocity according to the
exponential variation of eqn (5.8), various empirical modifications of the linear theory have
been proposed to improve the accuracy. One alternative is to use a linear extrapolation or
simply use a constant