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.

Second-order Stokes wave solutions for intefacial waves in three-layer stratified fluid with background current

In this paper, interfacial waves in three-layer stratified fluid with background current are investigated using a perturbation method, and the second-order asymptotic solutions of the velocity potentials and the second-order Stokes wave solutions of the associated elevations of the interfacial waves are presented based on the small amplitude wave theory, and the Kelvin-Helmholtz instability of interfacial waves is studied. As expected, for three-layer stratified fluid with background current, the first-order asymptotic solutions (linear wave solutions), dispersion relation and the second-order asymptotic solutions derived depend on not only the depths and densities of the three-layer fluid but also the background current of the fluids, and the second-order Stokes wave solutions of the associated elevations of the interfacial waves describe not only the second-order nonlinear wave-wave interactions between the interfacial waves but also the second-order nonlinear interactions between the interfacial waves and currents. It is also noted that the solutions obtained from the present work include the theoretical results derived by Chen et al (2005) as a special case. It also shows that with the given wave number k (real number) the interfacial waves may show Kelvin-Helmholtz instability.

The Interaction Between Shock Waves and Solid Spheres Arrays in a Shock Tube

When a shock wave interacts with a group of solid spheres, non-linear aerodynamic behaviors come into effect. The complicated wave reflections such as the Mach reflection occur in. the wave propagation process. The wave interactions with vortices behind each sphere's wake cause fluctuation in the pressure profiles of shock waves. This paper reports an experimental study for the aerodynamic processes involved in the interaction between shock waves and solid spheres. A schlieren photography was applied to visualize the various shock waves passing through solid spheres. Pressure measurements were performed along different downstream positions. The experiments were conducted in both rectangular and circular shock tubes. The data with respect to the effect of the sphere array, size, interval distance, incident Mach number, etc., on the shock wave attenuation were obtained.

Second-order solutions for random interfacial waves under steady uniform currents

In the present research, the study of Song (2004) for random interfacial waves in two-layer fluid is extended to the case of fluids moving at different steady uniform speeds. The equations describing the random displacements of the density interface and the associated velocity potentials in two-layer fluid are solved to the second order, and the wave-wave interactions of the wave components and the interactions between the waves and currents are described. As expected, the extended solutions include those obtained by Song (2004) as one special case where the steady uniform currents of the two fluids are taken as zero, and the solutions reduce to those derived by Sharma and Dean (1979) for random surface waves if the density of the upper fluid and the current of the lower fluid are both taken as zero.

Interactions of three dual-dressing effects of four-wave mixing in a five-level atomic system

We study the four-wave mixing (FWM) in an opening five-level system with two dressing fields. There are three kinds of doubly dressing mechanisms (parallel cascade, sequential cascade, and nested cascade) in the system for doubly dressed four-wave mixing. These mechanisms reflect different correlations between two dressing fields and different effects of two dressing fields to the FWM. Investigation of these mechanisms is helpful to understand the generated high-order nonlinear optical signal dressed by multi-fields.

Wave dynamic processes induced by a supersonic projectile discharging from a shock tube

A numerical study on wave dynamic processes occurring in muzzle blast flows, which are created by a supersonic projectile released from the open-end of a shock tube into ambient air, is described in this paper. The Euler equations, assuming axisymmetric flows, are solved by using a dispersion-controlled scheme implemented with moving boundary conditions. Three test cases are simulated for examining friction effects on the muzzle flow. From numerical simulations, the wave dynamic processes, including two blast waves, two jet flows, the bow shock wave and their interactions in the muzzle blasts, are demonstrated and discussed in detail. The study shows that the major wave dynamic processes developing in the muzzle flow remain similar when the friction varies, but some wave processes, such as shock-shock interactions, shock-jet interactions and the contact surface instability, get more intensive, which result in more complex muzzle blast flows.

Heating characteristics of blunt swept fin-induced shock wave turbulent boundary layer interaction

An experimental study was conducted on shock wave turbulent boundary layer interactions caused by a blunt swept fin-plate configuration at Mach numbers of 5.0, 7.8, 9.9 for a Reynolds number range of (1.0.similar to 4.7) x 10(7)/m. Detailed heat transfer and pressure distributions were measured at fin deflection angles of up to 30 degrees for a sweepback angle of 67.6 degrees. Surface oil flow patterns and liquid crystal thermograms as well as schlieren pictures of fin shock shape were taken. The study shows that the flow was separated at deflection of 10 degrees and secondary separation were detected at deflection of theta greater than or equal to 20 degrees. The heat transfer and pressure distributions on flat plate showed an extensive plateau region followed by a distinct dip and local peak close to the fin foot. Measurements of the plateau pressure and heat transfer were in good agreement with existing prediction methods, but pressure and heating peak measurements at M greater than or equal to 6 were significantly lower than predicted by the simple prediction techniques at lower Mach numbers.

Interaction of oblique incident electromagnetic wave with relativistic ionization front

Interactions of oblique incident probe wave with oncoming ionization fronts have been investigated using moving boundary conditions. Field conversion coefficients of reflection, transmission and magnetic modes produced in the interactions are derived. Phase matching conditions at the front and frequency up-shifting formulas for the three modes are also presented.

Spin precession and electron spin polarization wave in [001]-grown quantum wells

We theoretically study the spatial behaviors of spin precessions modulated by an effective magnetic field in a two-dimensional electron system with spin-orbit interaction. Through analysis of interaction between the spin and the effective magnetic field, we find some laws of spin precession in the system, by which we explain some previous phenomena of spin precession, and predict a controllable electron spin polarization wave in [001]-grown quantum wells. The shape of the wave, like water wave, mostly are ellipse-like or circle-like, and the wavelength is anisotropic in the quantum wells with two unequal coupling strengths of the Rashba and Dresselhaus interactions, and is isotropic in the quantum wells with only one spin orbit interaction.

Effects of Magnetohydrodynamic Interaction-Zone Position on Shock-Wave/Boundary-Layer Interaction

A third-order weighted essentially nonoscillatory and non-free-parameter difference scheme magnetohydrodynamic solver has been established to investigate the mechanisms of magnetohydrodynamics controlling separation induced by an oblique shock wave impinging on a flat plate. The effects of magnetohydrodynamic interaction-zone location on the separation point, reattachment point, separation-bubble size, and boundary-layer velocity profiles are analyzed. The results show that there exists a best location for the magnetohydrodynamic zone to be applied, where the separation point is delayed the farthest, and the separation bubble is decreased up to about 50% in size compared to the case without magnetohydrodynamic control, which demonstrated the promising of magnetohydrodynamics suppressing the separation induced by shock-wave/boundary-layer interactions.

Relativistic Distorted-Wave Collision Strengths of Ni-, Cu- and Zn-like Au Ions

Excitation energies and electron impact excitation strengths from the ground states of Ni-, Cu- and Zn-like Au ions are calculated. The collision strengths are computed by a 213-levels expansion for the Ni- like Au ion, 405-levels expansion for the Cu-like Au ion and 229-levels expansion for the Zn-like Au ion. Configuration interactions are taken into account for all levels included. The target state wavefunctions are calculated by using the Grasp92 code. The continuum orbits are computed in the distorted-wave approximation, in which the direct and exchange potentials among all the electrons are included. Excellent agreement is found when the results are compared with previous calculations and recent measurements.

Third-order Stokes wave solutions for interfacial internal waves in a three-layer density-stratified fluid

Interfacial internal waves in a three-layer density-stratified fluid are investigated using a singular method, and third-order asymptotic solutions of the velocity potentials and third-order Stokes wave solutions of the associated elevations of the interfacial waves are presented based on the small amplitude wave theory. as expected, the third-order solutions describe the third-order nonlinear modification and the third-order nonlinear interactions between the interfacial waves. The wave velocity depends on not only the wave number and the depth of each layer but also on the wave amplitude.

Simulation of the ocean surface mixed layer under the wave breaking

A one-dimensional mixed-layer model, including a Mellor-Yamada level 2.5 turbulence closure scheme, was implemented to investigate the dynamical and thermal structures of the ocean surface mixed layer in the northern South China Sea. The turbulent kinetic energy released through wave breaking was incorporated into the model as a source of energy at the ocean surface, and the influence of the breaking waves on the mixed layer was studied. The numerical simulations show that the simulated SST is overestimated in summer without the breaking waves. However, the cooler SST is simulated when the effect of the breaking waves is considered, the corresponding discrepancy with the observed data decreases up to 20% and the MLD calculated averagely deepens 3.8 m. Owing to the wave-enhanced turbulence mixing in the summertime, the stratification at the bottom of the mixed layer was modified and the temperature gradient spread throughout the whole thermocline compared with the concentrated distribution without wave breaking.

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.

Numerical Analysis of a Dual Polarization Mode-Locked Laser with a Quarter Wave Plate

Dynamical behaviors and frequency characteristics of an active mode-locked laser with a quarter wave plate (QWP) are numerically studied by using a set pf vectorial laser equation. Like a polarization self-modulated laser, a frequency shift of half the cavity mode spacing exists between the eigen-modes in the two neutral axes of QWP. Within the active medium, the symmetric gain and cavity structure maintain the pulse's circular polarization with left-hand and right-hand in turn for each round trip. Once the left-hand or right-hand circularly polarized pulse passes through QWP, its polarization is linear and the polarized direction is in one of the directions of i45o with respect to the neutral axes of QWP. The output components in the directions of i45" from the mirror close to QWP are all linearly polarized with a period of twice the round-trip time.