Wave Modelling

APPENDIX B – WAVE MODELLING AND LOADS

Wave Modelling

The spectral density of the sea elevation process may be represented by the JONSWAP
spectrum, see OS-J101. The JONSWAP spectrum describes wind sea conditions that are
reasonable for the most severe seastates. Moderate and low sea states in open sea areas,
not dominated by limited fetch, are often composed of both wind-sea and swell. Atwopeak
spectrum may be used to account for swell if this is of importance. The Ochi-Hubble
spectrum is a general two peak spectrum applicable for most areas. The Torsethaugen
spectrum is derived from specific North Sea data, see CN-30.5.
For near shore and shoreline wave energy devices, the evolution of the shape of the wave
spectra as the waves propagate into waters of finite depth shall betaken into account.
The Bretschneider and TMA wave spectrum can be used for shallow water. The TMA
spectrum is developed to incorporate finite depth effects into the JONSWAP spectrum. A
finite depth wave spectrum can also be obtained by multiplying an appropriate JONSWAP
spectrum by a shape function.
In deep water, the short-term probability distribution of the wave height H can be
assumedto follow a Rayleigh distribution. When predicting the probability of large waves
in shallow water for near shore devices, the Rayleigh probability density function (PDF)
will overestimate the probability of the expected wave. The reason for this is that the
Rayleigh PDF has a finite probability for any wave height, however in shallow water the
maximum height of any wave is limited by thewater depth. In shallow waters the wave
heights are limited by the water depth. The maximum wave height can be taken as 78 %
of the water depth. Use of the unmodified Rayleigh distribution for representation of the
distribution of wave heights in shallow waters is therefore on the conservative side.
Directionality of waves shall be considered for determination of wave height distributions
whensuch directionality has an impact on the design of the wave energy device.

Wave Kinematics

Non-Breaking Waves

The kinematics of regular waves may be described by analytical or numerical wave
theories. Wave theory and corresponding wave kinematics shall be selected according to
recognised methods with due consideration to actual water depth. Wave kinematics can
be described by linearwave theory for seastates with mild slopes, while Stokes wave
theories apply for steeper waves. The Stream Function or Boussinesq wave theories can
be used to represent the wave kinematics over a broad range of water depths. The
ranges of validity of the various wave theories are given in OS-J101. For large volume
floating structures where the wave kinematics is disturbed by the presence of thestructure, radiation diffraction analyses shall be performed.





Breaking Waves

Special attention should be given to breaking waves, where wave kinematics deviate
from those implied by the theories referred above. The kinematics of breaking wavesdepends on the type of breaking, surging, plunging or spilling breaker. The type of breaking is influenced by the ratio of deepwater steepnessto seabed slope, by windwave
interaction, wave-wave interaction and current interaction.
Spilling breakers are waves with minor breaking and which retain a steep-sided profile.
The kinematics of spilling breakers may be well described by the stream function wave
theory. Plunging breakers occur when a wave is made to break suddenly by running up a
seabed slope. The wave height of a plungingbreaker can be high above the limiting
regular wave height for the local water depth. The impinging of a plunging breaker on a
near shore or at shore wave energy device can lead to high impulsive loads and high local
pressures. An approximation of the horizontal water particle velocity between the still
water level and the wave crest is umax = 1.25 gh where h is the water depth and g is the...