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Environment: Modelling design waves |
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Environment: Modelling design waves |
Design wave heights and periods are commonly provided as a design input, but this is not always so, and the data are sometimes incomplete or in a different form from that required for OrcaFlex. For a comprehensive discussion see Tucker (1991), on which the following notes are based.
In the absence of measured wave data, the maximum storm can be estimated from wind statistics on the assumption that the waves are generated by the local winds. The governing parameters are fetch (the length of open water over which the wind blows), wind speed and duration. Significant wave height, $\Hs$, and average zero up-crossing period, $\Tz$, can then be estimated from equations given by Carter (1982):
\begin{align} \Hs &= 0.0163\ U X^{0.5} \\ \Tz &= 0.439\ U^{0.4} X^{0.3} \end{align}
\begin{align} \Hs &= 0.0146\ D^{5/7} U^{9/7} \\ \Tz &= 0.419\ D^{3/7} U^{4/7} \end{align} where $X$ is fetch in km, $U$ is wind speed in m/s at 10m above mean sea level, and $D$ is duration in hours.
The expected maximum wave height $H_\textrm{max}$ occurring in time $t$ in a storm of significant wave height $\Hs$, average zero crossing period $\Tz$ is given by \begin{equation} H_\textrm{max} = k \Hs \left(\tfrac12 \ln N\right)^{1/2} \end{equation} where $N = t/\Tz$ is the number of waves in the period under consideration. Most wave statistics are based on measurements taken at 3 hour intervals so $t$ should generally not be greater than 10800s.
The factor $k$ provides for the fact that the highest wave crest and deepest trough in any given storm do not in general occur together. The maximum crest-to-trough wave height is generally less than the sum of the maximum crest elevation plus maximum trough depth. Tucker recommends $k{=}0.9$ for the maximum wave (extreme storms) and $k{=}1.0$ for more moderate conditions (as used in fatigue analysis).
For extreme storms, K may be taken as 0.9, but for moderate wave conditions as used for fatigue analysis, K = 1 is usually assumed.
In extreme storm conditions, it is common to assume a significant wave steepness, $S$, of $1/18$ (with $\Hs$ in m, $\Tz$ in s), so \begin{equation} S = \frac{2\pi\Hs}{g\Tz^2} = \frac{1}{18} \end{equation} and hence, for an extreme storm \begin{equation} \Tz = \left(\frac{2\pi\Hs}{gS}\right)^{1/2} \approx 3.39\Hs^{1/2} \end{equation}
The period associated with the maximum wave, $T_\textrm{ass}$, can take a range of values. Tucker recommends \begin{equation} 1.05\Tz \lt T_\textrm{ass} \lt 1.40\Tz \end{equation} The spectral peak period $\Tp$ is sometimes specified instead of $\Tz$.
For the ISSC spectrum \begin{equation} \Tp = 1.41\Tz \end{equation} For the JONSWAP spectrum, the factor varies with the peak enhancement factor $\gamma$. The OrcaFlex random wave data form reports $\Tp$ and the spectral peak frequency $\fm{=}1/\Tp$.
For the mean JONSWAP spectrum, $\gamma{=}3.3$ and \begin{equation} \Tp = 1.29\Tz \end{equation}
For operations lasting from a few hours to a few days, different criteria apply. A typical requirement is to determine the maximum sea state in which a given operation can safely take place. Whilst the complete operation may take many hours or even days, critical parts such as landing an item of equipment on the seabed may only take a few minutes. It would be too conservative to apply 3 hour maximum conditions in such a case.
The question comes down to a balance of cost against risk. The overall risk of failure must be small enough to be acceptable (how small – 1%, 0.01%?), but the cost rises disproportionately as the level of acceptable risk is reduced. The risk of encountering a large wave is only one of many elements to be considered in assessing overall risk. This is a big subject which is rarely addressed rigorously.
There is a need here for some feedback from practical experience to determine what is in practice acceptable and what is not. Hindcasting of operations which took place successfully in what were judged to be marginal conditions, and of operations which were not successful due to adverse weather conditions could provide a calibrated basis for analysis of future operations. We do not know anyone who has done this – until they do, we are left with subjective judgement, i.e. we guess.
A commonly-used guess is to combine the significant wave (a regular wave of height $\Hs$, period $\Tz$ or $\Tp$ according to preference) for the assumed sea state with a maximum tidal current, applying both waves and current from the worst direction. This has no objective basis, but is plausible.