Obtaining the distribution of quiescent periods directly from the power spectral densities of Sea waves

There is a growing practical interest in the ability to increase the sea states at which marine operations can be safely undertaken by exploiting the quiescent periods that are well known to exist under a wide range of sea conditions. While the actual prediction of quiescent periods at sea for the control of operations is a deterministic process, the long term planning of future maritime tasks that rely on these quiescent periods is a statistical process involving the anticipated quiescence properties of the forecasted sea conditions in the geographical region of interest. It is in principle possible to obtain such data in tabular form either large scale simulation or from field data. However, such simulations are computationally intensive and libraries of appropriate field data are not common. Thus, it is clearly attractive to develop techniques that exploit standard wave spectral models for describing the quiescence statistics directly from such spectra. The present study focuses upon such techniques and is a first step towards the production of a computationally low-cost quiescence prediction tool and compares its efficacy against simulations. Two significant properties emerge for a large class of wave spectral models that encompasses the ubiquitous Neumann and Pierson Moskowitz or Bretschneider forms. Firstly, the auto-correlation function of the wave profile that are required to produce the quiescence property can be obtained analytically in terms of standard special functions. This considerably reduces the computational cost making desktop computer-based planning tools a reality. Secondly, for each class of these parametric spectra, the probability of a given number of consecutive wave heights (normalised to the significant wave heights) less than some critical value is in fact independent of absolute wave height. Thus, for a broad class of practically interesting wave spectra all that is required to obtain the statistical distribution of the quiescent periods is simple rescaling.