Page 112 - Pipelines and Risers

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Chapter 6

Hydrodynamics around Pipes

6.1 Wave Simulators

Wave simulators may be made, using 2D regular long-crested and 2D random long-crested
wave models. In each of the wave simulators, surface elevation, wave-induced water particle
velocity and acceleration, dynamical pressure and pressure gradient, of an arbitrary point in
space and time is defined mathematically. This allows the wave simulators to compute the
wave kinematics during a time-domain dynamic analysis.

6.2 Choice of Wave Theory

Comprehensive studies have been conducted to identify the most suitable wave theories for
representing the near-bottom kinematics due to wave action. In Dean et al. (1986) it was
concluded that linear wave theory provides a good prediction of near-bottom kinematics for a
wide range of relative water depth and wave steepness. One reason for this relatively good
agreement is that the influence of non-linearities considered in higher order wave theories is
reduced with depth below the free surface. In Kirkgoz (1986), it was also found that linear
wave theory gave acceptable predictions of near seabed water particle velocities in waves
close to the breaking point. It thus seems appropriate to apply linear wave theory to near
seabed objects for a wide range of wave heights, periods and water depths. The calculated
fluid velocities and accelerations of the surface waves, are transferred to seabed level using
linear wave theory.
The 2D regular long-crested waves are useful when investigating the effects of extreme
waves, while 2-D random long-crested waves are used when modeling a complete sea-state.

6.3 Mathematical Formulations used in the Wave Simulators

6.3.1 General
Most of the theory and formulas presented in this section are available from Faltinsen (1990),
Gran (1992), Hibbit et al. (1998) and Langen et al. (1997). This information has been used
when programming the three wave simulators using the WAVE subroutine in ABAQUS
(Hibbit et al. (1998)).