scholarly journals Level III Reliability Design of an Armor Block of Rubble Mound Breakwater Using Probabilistic Model of Wave Height Optimized for the Korean Sea Wave Conditions and Non-Gaussian Wave Slope Distribution

2021 ◽  
Vol 9 (2) ◽  
pp. 223
Author(s):  
Yong Jun Cho
Keyword(s):  
Wave Height ◽  
Gaussian Distribution ◽  
Wave Interaction ◽  
Numerical Results ◽  
Controversial Issues ◽  
Reliability Design ◽  
Resonant Wave ◽  
Wave Slope ◽  
Rubble Mound ◽  
Non Gaussian

In this study, a Level III reliability design of an armor block of rubble mound breakwater was developed using the optimized probabilistic wave height model for the Korean marine environment and Van der Meer equation. To demonstrate what distinguishes this study from the others, numerical simulation was first carried out, assuming that wave slope follows Gaussian distribution recommended by PIANC. Numerical results showed that Gaussian wave slope distribution overpredicted the failure probability of armor block, longer and shorter waves, and on the contrary, underpredicted waves of the medium period. After noting the limitations of Gaussian distribution, some efforts were made to develop an alternative for Gaussian distribution. As a result, non-Gaussian wave slope distribution was analytically derived from the joint distribution of wave amplitude and period by Longuet–Higgins using the random variables transformation technique. Numerical results showed that non-Gaussian distribution could effectively address the limitations of Gaussian distribution due to its capability to account for the nonlinear resonant wave–wave interaction and its effects on the wave slope distribution that significantly influences the armor block’s stability. Therefore, the non-Gaussian wave slope distribution presented in this study could play an indispensable role in addressing controversial issues such as whether or not enormous armor blocks like a Tetrapod of 100 t frequently mentioned in developing countermeasures against rough seas due to climate change is too conservatively designed.

scholarly journals On the Effects of Non-Gaussian Wave-Slope Distribution on the Failure Probability of an Armour block of Rubble Mound Breakwater

2021 ◽  
Vol 8 (3) ◽  
pp. 165-179
Author(s):  
Yong Jun Cho
Keyword(s):  
Numerical Simulation ◽  
Wave Height ◽  
Gaussian Distribution ◽  
Failure Probability ◽  
Maximum Likelihood Estimates ◽  
Random Wave ◽  
Height Distribution ◽  
Wave Slope ◽  
Rubble Mound ◽  
Non Gaussian

This study examined the effect of non-Gaussian wave slope distribution on the failure probability of an armoring rock of rubble mound breakwater using numerical simulation. Numerical simulation was carried out using the Van der Meer equation and Level III reliability design method based on the Monte Carlo simulation. In doing so, modified Glukhovskiy wave height distribution and situ wave height data collected at Ulleungdo from January 1, 1979-December 31, 2019 were used. Tri-modal Gaissuian wave slope distribution was also used, which showed good agreements with situ wave data collected at Mangbang from April 26, 2017, to April 20, 2018. The probability coefficients of tri-modal Gaussian distribution were estimated using Matlab-based statistics and machine learning toolbox, MLE [Maximum Likelihood Estimates]. In the numerical simulation, the intrinsic limitations of Gaussian distribution were revealed, such as imposing a non-negligible probability mass even in the negative wave slope, under-shooting in longer and shorter waves, and over-shooting in mid-scale waves. In the case of failure probability of an armoring rock, Gaussian distribution was shown to give underestimated failure probability. The extent of underestimation was more considerable at Mangbang, where a tidal terrace of lower depth and gently varying slope was developed than at Ulleungdo. These differences were triggered by the presence of probability plateau formed in wave slope distribution whenever infra-gravity waves appear in random wave packet due to the resonant wave-wave interaction. Therefore, it can be easily conceivable that probability plateau has a significant effect on the armoring rock failure probability. Therefore, PIANC's recommendation that wave slope follows Gaussian distribution needs to be amended. Moreover, the reliability-based design of breakwater should be implemented based on tri-modal Gaussian wave slope distribution, which can accurately reproduce probability plateau.

scholarly journals Mode Fluctuations as Fingerprints of Chaotic and Non-Chaotic Systems

1997 ◽  
Vol 11 (07) ◽  
pp. 805-849 ◽  
Author(s):  
R. Aurich ◽  
A. Bäcker ◽  
F. Steiner
Keyword(s):  
Gaussian Distribution ◽  
Integrable Systems ◽  
Chaotic Systems ◽  
Energy Levels ◽  
Numerical Results ◽  
Rigorous Results ◽  
Non Gaussian

The mode-fluctuation distribution P(W) is studied for chaotic as well as for non-chaotic quantum billiards. This statistic is discussed in the broader framework of the E(k,L) functions being the probability of finding k energy levels in a randomly chosen interval of length L, and the distribution of n(L), where n(L) is the number of levels in such an interval, and their cumulants ck(L). It is demonstrated that the cumulants provide a possible measure for the distinction between chaotic and non-chaotic systems. The vanishing of the normalized cumulants Ck, k ≥ 3, implies a Gaussian behaviour of P(W), which is realized in the case of chaotic systems, whereas non-chaotic systems display non-vanishing values for these cumulants leading to a non-Gaussian behaviour of P(W). For some integrable systems there exist rigorous proofs of the non-Gaussian behaviour which are also discussed. Our numerical results and the rigorous results for integrable systems suggest that a clear fingerprint of chaotic systems is provided by a Gaussian distribution of the mode-fluctuation distribution P(W).

scholarly journals Evolution of a Random Directional Wave and Freak Wave Occurrence

2009 ◽  
Vol 39 (3) ◽  
pp. 621-639 ◽  
Author(s):  
Takuji Waseda ◽  
Takeshi Kinoshita ◽  
Hitoshi Tamura
Keyword(s):  
Wave Height ◽  
Wave Interaction ◽  
Northwest Pacific ◽  
Frequency Bandwidth ◽  
Extreme Wave ◽  
Spectral Parameters ◽  
Freak Wave ◽  
Resonant Wave ◽  
Directional Wave ◽  
Wind Sea

Abstract The evolution of a random directional wave in deep water was studied in a laboratory wave tank (50 m long, 10 m wide, 5 m deep) utilizing a directional wave generator. A number of experiments were conducted, changing the various spectral parameters (wave steepness 0.05 < ɛ < 0.11, with directional spreading up to 36° and frequency bandwidth 0.2 < δk/k < 0.6). The wave evolution was studied by an array of wave wires distributed down the tank. As the spectral parameters were altered, the wave height statistics change. Without any wave directionality, the occurrence of waves exceeding twice the significant wave height (the freak wave) increases as the frequency bandwidth narrows and steepness increases, due to quasi-resonant wave–wave interaction. However, the probability of an extreme wave rapidly reduces as the directional bandwidth broadens. The effective Benjamin–Feir index (BFIeff) is introduced, extending the BFI (the relative magnitude of nonlinearity and dispersion) to incorporate the effect of directionality, and successfully parameterizes the observed occurrence of freak waves in the tank. Analysis of the high-resolution hindcast wave field of the northwest Pacific reveals that such a directionally confined wind sea with high extreme wave probability is rare and corresponds mostly to a swell–wind sea mixed condition. Therefore, extreme wave occurrence in the sea as a result of quasi-resonant wave–wave interaction is a rare event that occurs only when the wind sea directionality is extremely narrow.

scholarly journals Timing of Pubertal Onset in Girls: Evidence for Non-Gaussian Distribution

2008 ◽  
Vol 93 (11) ◽  
pp. 4422-4425 ◽  
Author(s):  
Anastasios Papadimitriou ◽  
Soula Pantsiotou ◽  
Konstandinos Douros ◽  
Dimitrios T. Papadimitriou ◽  
Polyxeni Nicolaidou ◽  
...  
Keyword(s):  
Gaussian Distribution ◽  
Pubertal Onset ◽  
Non Gaussian

scholarly journals Fatigue Life Analysis of Aluminum Alloy Notched Specimens under Non-Gaussian Excitation based on Fatigue Damage Spectrum

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Kuanyu Chen ◽  
Guangwu Yang ◽  
Jianjun Zhang ◽  
Shoune Xiao ◽  
Yang Xu
Keyword(s):  
Aluminum Alloy ◽  
Fatigue Life ◽  
Fatigue Damage ◽  
Relative Error ◽  
Gaussian Distribution ◽  
Calculation Method ◽  
Shaking Table ◽  
Notched Specimens ◽  
Acceleration Method ◽  
Non Gaussian

In this study, a non-Gaussian excitation acceleration method is proposed, using aluminum alloy notched specimens as a research object and measured acceleration signal of a certain airborne bracket, during aircraft flight as input excitations, based on the fatigue damage spectrum (FDS) theory. The kurtosis and skewness of the input signal are calculated and the non-Gaussian characteristics and amplitude distribution are evaluated. Five task segments obey a non-Gaussian distribution, while one task segment obeys a Gaussian distribution. The fatigue damage spectrum calculation method of non-Gaussian excitation is derived. The appropriate FDS calculation method is selected for each task segment and the acceleration parameters are set to construct the acceleration power spectral density, which is equivalent to the pseudo-acceleration damage. A finite-element model is established, the notch stress concentration factor of the specimen is calculated, the large mass point method is used to simulate the shaking table excitation, and a random vibration analysis is carried out to calculate the accelerated fatigue life. The simulation results show that the relative error between the original cumulative damage and test original fatigue life is 15.7%. The shaking table test results show that the relative error of fatigue life before and after acceleration is less than 16.95%, and the relative error of test and simulation is 24.27%. The failure time of the specimen is accelerated from approximately 12 h to 1 h, the acceleration ratio reaches 12, and the average acceleration ideal factor is 1.125, which verifies the effectiveness of the acceleration method. It provides a reference for the compilation of the load spectrum and vibration endurance acceleration test of other airborne aircraft equipment.

scholarly journals Decay Rates of Internal Tides Estimated by an Improved Wave–Wave Interaction Analysis

2018 ◽  
Vol 48 (11) ◽  
pp. 2689-2701 ◽  
Author(s):  
Yohei Onuki ◽  
Toshiyuki Hibiya
Keyword(s):  
Kinetic Equation ◽  
Energy Loss ◽  
Interaction Analysis ◽  
Wave Interaction ◽  
Deep Ocean ◽  
Energy Decay ◽  
Decay Rates ◽  
Internal Tides ◽  
Global Ocean ◽  
Resonant Wave

AbstractRecent numerical and observational studies have reported that resonant wave–wave interaction may be a crucial process for the energy loss of internal tides and the associated vertical water mixing in the midlatitude deep ocean. Special attention has been directed to the remarkable latitudinal dependence of the resonant interaction intensity; semidiurnal internal tides promptly lose their energy to near-inertial motions through parametric subharmonic instability equatorward of the critical latitudes 29°N/S, where half the tidal frequency coincides with the local inertial frequency. This feature contradicts the classical theoretical prediction that resonant wave–wave interaction does not play a major role in the tidal energy loss in the open ocean. By reformulating the kinetic equation for long internal waves and developing its calculation method, we estimate the energy decay rates of the low-vertical-mode semidiurnal internal tides interacting with the “ubiquitous” oceanic internal wave field. The result shows rapid energy decay of the internal tides, typically within O(10) days for the lowest-mode component, near their critical latitudes. This decay time is severalfold shorter than those in the classical studies and, additionally, varies by a factor of 2 depending on the local depth and density structure. We suggest from this study that the numerical integration of the kinetic equation is a more effective approach than recognized to determine the decay parameter of wave energy, which is indispensable for the global ocean models.

scholarly journals The Spectral Power Density and Shadowing Function of a Glacial Microrelief at the Decimetre Scale

1979 ◽  
Vol 23 (89) ◽  
pp. 57-66 ◽  
Author(s):  
J.-P. Benoist
Keyword(s):  
Power Density ◽  
Gaussian Distribution ◽  
Spectral Power ◽  
Spectral Power Density ◽  
Total Length ◽  
Theoretical Function ◽  
Significant Difference ◽  
Longitudinal Profiles ◽  
Non Gaussian

Abstract Longitudinal profiles of roches moutonnées have been measured once every centimetre over a total length of more than 100 m. Only wavelengths in the range 3.6 cm < λ < 40 cm have been kept and analysed. Levels and their slopes have a symmetrical, non-Gaussian distribution. The spectral power density varies roughly as γ 0 ν–n (ν ═ wavenumber ═ 1/λ); n being the same for all the profiles (n ═ 2.36) and γ 0 being dependent on the studied area. No significant difference has been found for the shadowing function of the different studied areas. It differs consistently from Smith’s theoretical function.

Study on the mutual influence of surface roughness and texture features of rough-textured surfaces on the tribological properties

2020 ◽  
pp. 135065012094021
Author(s):  
Chunxing Gu ◽  
Xianghui Meng ◽  
Shuwen Wang ◽  
Xiaohong Ding
Keyword(s):  
Surface Roughness ◽  
Tribological Properties ◽  
Gaussian Distribution ◽  
Mutual Influence ◽  
Surface Texturing ◽  
Texture Features ◽  
Tribological Performance ◽  
Mixed Lubrication ◽  
Non Gaussian ◽  
Skewness And Kurtosis

In recent years, the efforts to better control friction and wear have focused on surface topography modification through surface texturing. To study the mutual influence of surface roughness and texture features, this paper developed one comprehensive mathematical model of mixed lubrication to study the tribological performance of the rough-textured conjunction. The typical ring-liner conjunction was chosen as the research object. In particular, the effects of skewness and kurtosis were considered based on the non-Gaussian distribution of asperity height. In this way, the influences of non-Gaussian distribution properties and surface texturing on the tribological performance were analyzed. The results show that the influences of skewness and kurtosis on the tribological performance are nontrivial and should not be neglected in the mixed lubrication. Compared to the Gaussian distribution, considering the non-Gaussian distribution can represent the physical rough surfaces more accurately. Surfaces with negative skewness were found to generally result in better tribological properties. Moreover, the tribological performance improved by surface texturing can also be improved or reduced by the effect of skewness and kurtosis. As a result, the optimization of surface texturing should take the effects of roughness parameters into account.

Sign in / Sign up

Export Citation Format

Share Document