Second-order solutions for random interfacial waves in N-layer density-stratified fluid with steady uniform currents

In the present paper, the random inter facial waves in N-layer density-stratified fluids moving at different steady uniform speeds are researched by using an expansion technique, and the second-order a symptotic solutions of the random displacements of the density interfaces and the associated velocity potentials in N-layer fluid are presented based on the small amplitude wave theory. The obtained results indicate that the wave-wave second-order nonlinear interactions of the wave components and the second-order nonlinear interactions between the waves and currents are described. As expected, the solutions include those derived by Chen (2006) as a special case where the steady uniform currents of the N-layer fluids are taken as zero, and the solutions also reduce to those obtained by Song (2005) for second-order solutions for random interfacial waves with steady uniform currents if N=2.

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.