Probability Distributions Of Wave Height Research Articles

Offshore Structural Reliability Assessment by Probabilistic Procedures—A Review

Offshore installations must be built to resist fatigue as well as extreme forces caused by severe environmental conditions. The structural reliability analysis is the popular practise to assess a variety of natural waves determined by the long-term probability distribution of wave heights and corresponding periods on the site. In truth, however, these structures are subjected to arbitrary wave-induced forces in the open ocean. Hence, it is much more reasonable to account for the changed loading characteristics by determining the probabilistic characteristics of the random loads and outcomes responses. The key challenges are uncertainties and the non-linearity of Morison’s drag element, which results in non-Gaussian loading and response distributions. This study would analyze advances achieved to date in a comprehensive probabilistic review of offshore fixed jacket-type platforms.

Experimental study of breathers and rogue waves generated by random waves over non-uniform bathymetry

We present experimental evidence of formation and persistence of localized waves, breathers, and solitons, occurring in a random sea state and uniformly traveling over non-uniform bathymetry. Recent studies suggest connections between breather dynamics and irregular sea states and between extreme wave formation and breathers, random sea states, or non-uniform bathymetry individually. In this paper, we investigate the joint connection between these phenomena, and we found that breathers and deep-water solitons can persist in more complex environments. Three different sets of significant heights have been generated within a Joint North Sea Wave Observation Project wave spectrum, and the wave heights were recorded with gauges in a wave tank. Statistical analysis was applied to the experimental data, including the space and time distribution of kurtosis, skewness, Benjamin–Feir index, moving Fourier spectra, and probability distribution of wave heights. Stable wave packages formed out of the random wave field and traveling over shoals, valleys, and slopes were compared with exact solutions of the nonlinear Schrödinger equation with a good match, demonstrating that these localized waves have the same structure as deep-water breathers. We identify the formation of rogue waves at moments and over regions where the kurtosis and skewness have local maxima. These results provide insights for understanding of the robustness of Peregrine and higher-order Akhmediev breathers, Kuznetsov–Ma solitons, and rogue waves, and their occurrence in realistic oceanic conditions, and may motivate analogous studies in other fields of physics to identify limitations of exact weakly nonlinear models in non-homogeneous media.

Effect of wave spectrum width on the probability density distribution of wind-wave heights

The probability distribution of wave heights under the assumption of narrowband linear wave theory follows the Rayleigh distribution and the statistical relationships between some characteristic wave heights, derived from this distribution, are widely used for the treatment of realistic wind waves. However, the bandwidth of wave frequency influences the probability distribution of wave heights. In this paper, a wave-spectrum-width parameter B was introduced into the JONSWAP spectrum. This facilitated the construction of a wind-wave spectrum and the reconstruction of wind-wave time series for various growth stages, based on which the probability density distributions of the wind-wave heights were studied statistically. The distribution curves deviated slightly from the theoretical Rayleigh distribution with increasing B. The probability that a wave height exceeded a certain value was clearly smaller than the theoretical value for Ba parts per thousand yen0.3, and the difference between them increased with the threshold value. The relation between the H (s)/sigma ratio and B was investigated statistically, which revealed that the H (s)/sigma ratio deviated from 4.005 and declined with B. When B reached 0.698 1, the H (s)/sigma ratio was 3.825, which is about 95.5% of its original value. This indicates an overestimation in the prediction of H (s) from H (s)=4.005 sigma, and provides a potential method for improving the accuracy of the H (s) remote sensing retrieval algorithm, critical for extremely large waves under severe sea states.

Probability distribution of wave heights attenuated by salt marsh vegetation during tropical cyclone

Zero-crossing wave heights, obtained from the field measurement of random waves propagating through salt marsh vegetation (Spartina alterniflora) during a tropical storm, were analyzed to examine their probability distribution. Wave data (significant wave heights up to 0.4m in 0.8m depth) were collected over a two-day period along a 28m transect using three pressure transducers sampling at 10Hz. Wave height distribution was observed to deviate from the Rayleigh distribution. The observed probability densities of the larger wave heights were reduced significantly by vegetation, producing wave heights lower than those predicted by the Rayleigh distribution. Assuming Rayleigh distributed wave heights for the incident waves to the vegetation patch, existing vegetation-induced wave attenuation formulations are used to derive a special form of two-parameter Weibull distribution for wave heights in the inundated wetland. The scale parameter of the distribution is theoretically shown to be a function of the shape parameter, which agrees with the measurements, effectively reducing the proposed distribution to a one-parameter type. The derived distribution depends on the local parameters only and fits well to the observed distribution of wave heights attenuated by vegetation. Empirical relationships are developed to estimate the shape parameter from the local wave parameters.

Linear and nonlinear rogue wave statistics in the presence of random currents*** This invited article is one of a series published throughout 2011 in Nonlinearity on the topic of Rogue Waves.

We review recent progress in modelling the probability distribution of wave heights in the deep ocean as a function of a small number of parameters describing the local sea state. Both linear and nonlinear mechanisms of rogue wave formation are considered. First, we show that when the average wave steepness is small and nonlinear wave effects are subleading, the wave height distribution is well explained by a single ‘freak index’ parameter, which describes the strength of (linear) wave scattering by random currents relative to the angular spread of the incoming random sea. When the average steepness is large, the wave height distribution takes a very similar functional form, but the key variables determining the probability distribution are the steepness, and the angular and frequency spread of the incoming waves. Finally, even greater probability of extreme wave formation is predicted when linear and nonlinear effects are acting together.

Probability Distributions of Wave Heights and Periods in Measured Combined Sea-States from the Portuguese Coast

An analysis is made of measured two-peaked sea spectra from a deep-water location at the Portuguese Coast. The spectra are organized in different groups according to the relative nature of their two component wave systems. The probability distributions of wave height and period are determined and compared with several theoretical models.

Estimacion de los valores de retorno de la altura de ola en la Provincia de Buenos Aires, Argentina

The wave height recorded at 8 stations along the oceanic coast of the Province of Buenos Aires, Argentina, was analysed to estimate the 50-year return value of wave height at each station. The probability distributions of wave height for the measurements made at Mar de Ajó (1976/85), punta Médanos (northern and southern waveriders, 1981/84), Pinamar (1976/91), Mar del Plata (1968/69), Puerto Quequén (1975/76), Pehuen-Có (1986/88) and El Cóndor (1988) summer resort were tested with the theoretical distributions of Rayleigh, Weibull and Fisher-Tippett I. Excluding Mar de Ajó and El Cóndor, the best fit was obtained with the Fisher-Tippett probability density function. The method of Battjes for estimating the return values of wave height was applied and the resulting 50-year return values were 2.80; 6.90; 7.90; 7.20; 7.21; 8.20; 4.30 and 2.84 m for Mar de Ajó, punta Médanos (northern waverider), punta Médanos (southern waverider), Pinamar, Mar del Plata, Puerto Quequén, Pehuen-Có and El Cóndor, respectively. Lastly, the standard method of extreme values was used to analyse 10 and 16 annual wave height maxima from Mar de Ajó and Pinamar, respectively. The 50-year return values were found to be 2.30 m for Mar de Ajó and 7.20 m for Piramar.

Calculations of wave breaking probability and distribution of breaking wave heights in deep water

This practical method for calculating the probability of a wave breaking and the distribution of breaking wave heights is based on the joint probability distribution of wave heights and periods derived by Sun Fu and the breaking criterion obtained by Ochi and Tsai from measurements of irregular waves generated in a tank. Computations for different sea states using the P-M spectrum and the JONSWAP spectrum showed that the probability of wave breaking (or the distribution of breaking wave heights) in the deep ocean can be determined, at least approximated, from the zero, the first and the second moments of the wave spectrum.

Breaking-Limited Wave Heights

Empirical distributions of wave heights derived from field data differ from the theoretical distribution of wave heights as given by the Rayleigh law. A principal cause of this discrepancy is suggested to be that the conventional theory does not in any way account for wave breaking. Based on the assumption that the sea surface is characterized with a narrow-band spectrum, the probability distribution of wave heights limited by breaking, due to a Stokes-type limiting steepness in deep or finite water depths, is derived. The breaking-limited distribution provides a probability discription which compares with two well documented field observations more favorably than the Rayleigh law.