Statistical distribution of depth-integrated local horizontal momentum for second-order random ocean waves in finite water depth

Based on the second-order random wave solutions of water wave equations in finite water depth, statistical distributions of the depth- integrated local horizontal momentum components are derived by use of the characteristic function expansion method. The parameters involved in the distributions can be all determined by the water depth and the wave-number spectrum of ocean waves. As an illustrative example, a fully developed wind-generated sea is considered and the parameters are calculated for typical wind speeds and water depths by means of the Donelan and Pierson spectrum. The effects of nonlinearity and water depth on the distributions are also investigated.

Statistical distribution of wave-surface elevation for second-order random directional ocean waves in finite water depth

Based on the second-order random wave solutions of water wave equations in finite water depth, a statistical distribution of the wave-surface elevation is derived by using the characteristic function expansion method. It is found that the distribution, after normalization of the wave-surface elevation, depends only on two parameters. One parameter describes the small mean bias of the surface produced by the second-order wave-wave interactions. Another one is approximately proportional to the skewness of the distribution. Both of these two parameters can be determined by the water depth and the wave-number spectrum of ocean waves. As an illustrative example, we consider a fully developed wind-generated sea and the parameters are calculated for various wind speeds and water depths by using Donelan and Pierson spectrum. It is also found that, for deep water, the dimensionless distribution reduces to the third-order Gram-Charlier series obtained by Longuet-Higgins [J. Fluid Mech. 17 (1963) 459]. The newly proposed distribution is compared with the data of Bitner [Appl. Ocean Res. 2 (1980) 63], Gaussian distribution and the fourth-order Gram-Charlier series, and found our distribution gives a more reasonable fit to the data. (C) 2002 Elsevier Science B.V. All rights reserved.

Statistical distribution of nonlinear random wave height

A statistical model of random wave is developed using Stokes wave theory of water wave dynamics. A new nonlinear probability distribution function of wave height is presented. The results indicate that wave steepness not only could be a parameter of the distribution function of wave height but also could reflect the degree of wave height distribution deviation from the Rayleigh distribution. The new wave height distribution overcomes the problem of Rayleigh distribution that the prediction of big wave is overestimated and the general wave is underestimated. The prediction of small probability wave height value of new distribution is also smaller than that of Rayleigh distribution. Wave height data taken from East China Normal University are used to verify the new distribution. The results indicate that the new distribution fits the measurements much better than the Rayleigh distribution.

Probability distribution of random wave-current forces

Based on the second-order solutions obtained for the three-dimensional weakly nonlinear random waves propagating over a steady uniform current in finite water depth, the joint statistical distribution of the velocity and acceleration of the fluid particle in the current direction is derived using the characteristic function expansion method. From the joint distribution and the Morison equation, the theoretical distributions of drag forces, inertia forces and total random forces caused by waves propagating over a steady uniform current are determined. The distribution of inertia forces is Gaussian as that derived using the linear wave model, whereas the distributions of drag forces and total random forces deviate slightly from those derived utilizing the linear wave model. The distributions presented can be determined by the wave number spectrum of ocean waves, current speed and the second order wave-wave and wave-current interactions. As an illustrative example, for fully developed deep ocean waves, the parameters appeared in the distributions near still water level are calculated for various wind speeds and current speeds by using Donelan-Pierson-Banner spectrum and the effects of the current and the nonlinearity of ocean waves on the distribution are studied. (c) 2006 Elsevier Ltd. All rights reserved.

Tandem duplication-random loss is not a real feature of oyster mitochondrial genomes

Duplications and rearrangements of coding genes are major themes in the evolution of mitochondrial genomes, bearing important consequences in the function of mitochondria and the fitness of organisms. Yu et al. (BMC Genomics 2008, 9: 477) reported the complete mt genome sequence of the oyster Crassostrea hongkongensis (16,475 bp) and found that a DNA segment containing four tRNA genes (trnK(1), trnC, trnQ(1) and trnN), a duplicated (rrnS) and a split rRNA gene (rrnL5') was absent compared with that of two other Crassostrea species. It was suggested that the absence was a novel case of "tandem duplication-random loss" with evolutionary significance. We independently sequenced the complete mt genome of three C. hongkongensis individuals, all of which were 18,622 bp and contained the segment that was missing in Yu et al.'s sequence. Further, we designed primers, verified sequences and demonstrated that the sequence loss in Yu et al.'s study was an artifact caused by placing primers in a duplicated region. The duplication and split of ribosomal RNA genes are unique for Crassostrea oysters and not lost in C. hongkongensis. Our study highlights the need for caution when amplifying and sequencing through duplicated regions of the genome.

An New Area Function for Sharp indenter Tips in Nanoindentation

A new area function is introduced and applied to a Berkovich tip in order to characterize the contact projected area between an indenter and indented material. The function can be related directly to tip-rounding, thereby having obviously physical meaning. Nanoindentation experiments are performed on a commercial Nano Indenter XPsystem. The other two area functions introduced by Oliver and Pharr and by Thurn and Cook respectively are involved in this paper for comparison. By comparison from experimental results among different area functions, the indenter tip described by the proposed area function here is very close to the experimental indenter.

Simulations and Experiments of Stochastic Characteristics for Collective Short Fatigue Cracks in Steels

Stochastic characteristics prevail in the process of short fatigue crack progression. This paper presents a method taking into account the balance of crack number density to describe the stochastic behaviour of short crack collective evolution. The results from the simulation illustrate the stochastic development of short cracks. The experiments on two types of steels show the random distribution for collective short cracks with the number of cracks and the maximum crack length as a function of different locations on specimen surface. The experiments also give the variation of total number of short cracks with fatigue cycles. The test results are consistent with numerical simulations.

Ice induced low temperature fatigue crack propagation in offshore structural steel A131

To investigate the low temperature fatigue crack propagation behavior of offshore structural steel A131 under random ice loading, three ice failure modes that are commonly present in the Bohai Gulf are simulated according to the vibration stress responses induced by real ice loading. The test data are processed by a universal software FCPUSL developed on the basis of the theory of fatigue crack propagation and statistics. The fundamental parameter controlling the fatigue crack propagation induced by random ice loading is determined to be the amplitude root mean square stress intensity factor K-arm. The test results are presented on the crack propagation diagram where the crack growth rate da/dN is described as the function of K-arm. It is evident that the ice failure modes have great influence on the fatigue crack propagation behavior of the steel in ice-induced vibration. However, some of the experimental phenomena and test results are hard to be physically explained at present. The work in this paper is an initial attempt to investigate the cause of collapse of offshore structures due to ice loading.

Dynamic function of damage and its implications

Dynamic function of damage is the key to the problem of damage evolution of solids. In order to understand it, one must understand its mesoscopic mechanisms and macroscopic formulation. In terms of evolution equation of microdamage and damage moment, a dynamic function of damage is strictly defined. The mesoscopic mechanism underlying self-closed damage evolution law is investigated by means of double damage moments. Numerical results of damage evolution demonstrate some common features for various microdamage dynamics. Then, the dynamic function of damage is applied to inhomogeneous damage field. In this case, damage evolution rate is no longer equal to the dynamic function of damage. It is found that the criterion for damage localization is closely related to compound damage. Finally, an inversion of damage evolution to the dynamic function of damage is proposed.