Joint Distribution Of Heights Research Articles

The joint distribution of heights and periods of shoaling waves

The evolution of the joint distribution of wave heights and periods that results from shoaling is investigated using laboratory data obtained from experiments conducted on two (1:40 and 1:20) planar beach slopes. The data are compared to the theoretical joint distribution for wave heights and periods proposed by Longuet‐Higgins (1983). For unbroken waves with d/L >≈ 0.1 the shapes of the observed and predicted distributions agree reasonably well. However, the predicted joint distribution given by Longuet‐Higgins (1983) is displaced relative to the observed distribution. A parameterization for the observed displacement is offered. In addition, a parameterization for the variation of the spectral width parameter through the shoaling region is also given.

Abelian sandpile model on the Bethe lattice

The authors study Bak, Tang and Wiesenfeld's Abelian sandpile model (1987) of self-organised criticality on the Bethe lattice. Exact expressions for various distribution functions including the height distribution at a site and the joint distribution of heights at two sites separated by an arbitrary distance are obtained. They also determine the probability distribution of the number of distinct sites that topple at least once, the number of toplings at the origin and the total number of toplings in an avalanche. The probability that an avalanche consists of more than n toplings varies as n-1/2 for large n. The probability that its duration exceeds T decreases as 1/T for large T. These exponents are the same as for the critical percolation clusters in mean field theory.

On the joint distribution of heights and periods of sea waves

In the design of offshore structures, a consistent method of choosing the height and period for the adopted design wave may be crucial for a reliable design. With this objective, the joint probability density function for the height and period is considered in this paper. At first the adequacy of a simple theoretical model for the joint distribution under stationary conditions is investigated, using measurements achieved during storms in Northern North Sea. In a slightly modified form the model is found to be of a reasonable accuracy as far as the highest waves are of interest. Design curves regarding simultaneous values of heights and periods are estimated by means of this model and their possible impact for design is discussed.

On spectral and statistical characteristics of shallow water waves

Spectral, zero up-crossing and Tucker's methods of analysis are examined for shallow water wave records. Among the wave height parameters H s and H _- are most reliable and consistent irrespective of the analysis technique. Tucker analysis, though simple, seems versatile for estimating these wave height parameters. The standard period parameters are less consistent. For practical purposes every period that might reasonably occur has to be considered along with their corresponding height estimate. Joint distribution of heights and periods is in agreement with the function proposed by CNEXO.