Wave Kinematics |
 
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Wave Kinematics |
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Linear Airy wave theory is strictly valid only for infinitesimal wave heights. A number of modifications have been proposed to modify Airy wave theory for finite amplitude waves, and three of these are incorporated into Flexcom. The wave kinematics algorithms available are:
•Vertical Stretching
oKinematics above the MWL (mean water level) are assumed equal to those at the MWL
•Wheeler Stretching
oMWL kinematics are extended/stretched up to the wave surface
o*WAVE-GENERAL -> OPTION=EXTENDED
•Superposition/Extrapolation Stretching
oMWL kinematics are extrapolated up to the wave surface
oDefault option in Flexcom
There is no compelling theoretical justification for any of the three kinematics options, and there is no sense in which one is more correct than the other. The choice between them is a matter of engineering judgement. In general, the default option results in the largest wave forces, and can be considered the most conservative.
The theoretical basis of each for the algorithms is as follows. The term E(z) is a scaling factor which can be represented mathematically as follows:
where k is the wave number, d is the MWL and z is the distance above the MWL. The following hyperbolic function are defined mathematically as follows:
and
Vertical Stretching
This specific type of wave stretching has the effect of setting the kinematics above the MWL the be the same as those existing at a depth of d.
Vertical Stretching
Wheeler Stretching
This method tends to stretch or compress the water column linearly to such a height that is equivalent to the MWL. This can be achieved be substituting E(z) with E(z'):
where ζ is the z-value at the current water surface, Thus, E(z') can be written as follows:
Wheeler Stretching
Extrapolation Stretching
This method's mechanism extends E(z) to distances above the MWL. This is achieved by employing linear extrapolation of the tangent to E(z) at the MWL. This is expressed mathematically as follows for z<0:
However, for z>0, E(z)=E(0)+zE'(0):
Superposition Stretching
•*WAVE-GENERAL is used to specify miscellaneous parameters to wave loading. Specifically, the OPTION= input is used to specify the algorithm to be used by Flexcom in calculating Airy wave kinematics.
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