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.

Mud mass transport due to waves based on an empirical rheology model featured by hysteresis loop

A vertical 2-D water-mud numerical model is developed for estimating the rate of mud mass transport under wave action. A nonlinear semi-empirical rheology model featured by remarkable hysteresis loops in the relationships of the shear stress versus both the shear strain and the rate of shear strain of mud is applied to this water mud model. A logarithmic grid in the vertical direction is employed for numerical treatment, which increases the resolution of the flow in the neighborhood of both sides of the interface. Model verifications are given through comparisons between the calculated and the measured mud mass transport velocities as well as wave height changes. (C) 2006 Elsevier Ltd. All rights reserved.

A study of internal solitary waves observed on the continental shelf in the northwestern South China Sea

Based on in-situ time series data from the acoustic Doppler current profiler (ADCP) and thermistor chain in Wenchang area, a sequence of internal solitary wave (ISW) packets was observed in September 2005, propagating northwest on the continental shelf of the northwestern South China Sea (SCS). Corresponding to different stratification of the water column and tidal condition, both elevation and depression ISWs were observed at the same mooring location with amplitude of 35 m and 25 m respectively in different days. Regular arrival of the remarkable ISW packets at approximately the diurnal tidal period and the dominance of diurnal internal waves in the study area, strongly suggest that the main energy source of the waves is the diurnal tide. Notice that the wave packets were all riding on the troughs and shoulders of the internal tides, they were probably generated locally from the shelf break by the evolution of the internal tides due to nonlinear and dispersive effects.

Roles of equatorial waves and western boundary reflection in the seasonal circulation of the equatorial Indian Ocean

An ocean general circulation model (OGCM) is used to study the roles of equatorial waves and western boundary reflection in the seasonal circulation of the equatorial Indian Ocean. The western boundary reflection is defined as the total Kelvin waves leaving the western boundary, which include the reflection of the equatorial Rossby waves as well as the effects of alongshore winds, off-equatorial Rossby waves, and nonlinear processes near the western boundary. The evaluation of the reflection is based on a wave decomposition of the OGCM results and experiments with linear models. It is found that the alongshore winds along the east coast of Africa and the Rossby waves in the off-equatorial areas contribute significantly to the annual harmonics of the equatorial Kelvin waves at the western boundary. The semiannual harmonics of the Kelvin waves, on the other hand, originate primarily from a linear reflection of the equatorial Rossby waves. The dynamics of a dominant annual oscillation of sea level coexisting with the dominant semiannual oscillations of surface zonal currents in the central equatorial Indian Ocean are investigated. These sea level and zonal current patterns are found to be closely related to the linear reflections of the semiannual harmonics at the meridional boundaries. Because of the reflections, the second baroclinic mode resonates with the semiannual wind forcing; that is, the semiannual zonal currents carried by the reflected waves enhance the wind-forced currents at the central basin. Because of the different behavior of the zonal current and sea level during the reflections, the semiannual sea levels of the directly forced and reflected waves cancel each other significantly at the central basin. In the meantime, the annual harmonic of the sea level remains large, producing a dominant annual oscillation of sea level in the central equatorial Indian Ocean. The linear reflection causes the semiannual harmonics of the incoming and reflected sea levels to enhance each other at the meridional boundaries. In addition, the weak annual harmonics of sea level in the western basin, resulting from a combined effect of the western boundary reflection and the equatorial zonal wind forcing, facilitate the dominance by the semiannual harmonics near the western boundary despite the strong local wind forcing at the annual period. The Rossby waves are found to have a much larger contribution to the observed equatorial semiannual oscillations of surface zonal currents than the Kelvin waves. The westward progressive reversal of seasonal surface zonal currents along the equator in the observations is primarily due to the Rossby wave propagation.

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.

A kind of extended Korteweg-de Vries equation and solitary wave solutions for interfacial waves in a two-fluid system

This paper considers interfacial waves propagating along the interface between a two-dimensional two-fluid with a flat bottom and a rigid upper boundary. There is a light fluid layer overlying a heavier one in the system, and a small density difference exists between the two layers. It just focuses on the weakly non-linear small amplitude waves by introducing two small independent parameters: the nonlinearity ratio epsilon, represented by the ratio of amplitude to depth, and the dispersion ratio mu, represented by the square of the ratio of depth to wave length, which quantify the relative importance of nonlinearity and dispersion. It derives an extended KdV equation of the interfacial waves using the method adopted by Dullin et al in the study of the surface waves when considering the order up to O(mu(2)). As expected, the equation derived from the present work includes, as special cases, those obtained by Dullin et al for surface waves when the surface tension is neglected. The equation derived using an alternative method here is the same as the equation presented by Choi and Camassa. Also it solves the equation by borrowing the method presented by Marchant used for surface waves, and obtains its asymptotic solitary wave solutions when the weakly nonlinear and weakly dispersive terms are balanced in the extended KdV equation.

Identification of nonlinear dynamic systems: Time-frequency filtering and skeleton curves

The nonlinear behavior varying with the instantaneous response was analyzed through the joint time-frequency analysis method for a class of S. D. O. F nonlinear system. A masking operator an definite regions is defined and two theorems are presented. Based on these, the nonlinear system is modeled with a special time-varying linear one, called the generalized skeleton linear system (GSLS). The frequency skeleton curve and the damping skeleton curve are defined to describe the main feature of the non-linearity as well. Moreover, an identification method is proposed through the skeleton curves and the time-frequency filtering technique.

Numerical Investigation of Richtmyer-Meshkov Instability Driven by Cylindrical Shocks

In this paper, a numerical method with high order accuracy and high resolution was developed to simulate the Richtmyer-Meshkov(RM) instability driven by cylindrical shock waves. Compressible Euler equations in cylindrical coordinate were adopted for the cylindrical geometry and a third order accurate group control scheme was adopted to discretize the equations. Moreover, an adaptive grid technique was developed to refine the grid near the moving interface to improve the resolution of numerical solutions. The results of simulation exhibited the evolution process of RM instability, and the effect of Atwood number was studied. The larger the absolute value of Atwood number, the larger the perturbation amplitude. The nonlinear effect manifests more evidently in cylindrical geometry. The shock reflected from the pole center accelerates the interface for the second time, considerably complicating the interface evolution process, and such phenomena of reshock and secondary shock were studied.

Micro-shock waves generated inside a fluid jet impinging on plane wall

An Nd:glass laser pulse (18 ns, 1.38 J) is focused in a tiny area of about 100-mum diam under ambient conditions to produce micro-shock waves. The laser is focused above a planar surface with a typical standoff distance of about 4 mm, The laser energy is focused inside a supersonic circular jet of carbon dioxide gas produced by a nozzle with internal diameter of 2.9 mm and external diameter of 8 mm, Nominal value of the Mach number of the jet is around 2 with the corresponding pressure ratio of 7.5 (stagnation pressure/static pressure at the exit of the nozzle), The interaction process of the micro-shock wave generated inside the supersonic jet with the plane wall is investigated using double-pulse holographic interferometry. A strong surface vortex field with subsequent generation of a side jet propagating outward along the plane wail is observed. The interaction of the micro-shock wave with the cellular structure of the supersonic jet does not seem to influence the near surface features of the flowfield. The development of the coherent structures near the nozzle exit due to the upstream propagation of pressure waves seems to be affected by the outward propagating micro-shock wave. Mach reflection is observed when the micro-shock wave interacts with the plane wall at a standoff distance of 4 mm, The Mach stem is slightly deflected, indicating strong boundary-layer and viscous effects near the wall. The interaction process is also simulated numerically using an axisymmetric transient laminar Navier-Stokes solver. Qualitative agreement between experimental and numerical results is good.

Dynamic Characteristics of Spherically Converging Detonation Waves

The spherically converging detonation wave was numerically investigated by solving the one-dimensional multi-component Euler equations in spherical coordinates with a dispersion-controlled dissipative scheme. Finite rate and detailed chemical reaction models were used and numerical solutions were obtained for both a spherical by converging detonation in a stoichiometric hydrogen-oxygen mixture and a spherically focusing shock in air. The results showed that the post-shock pressure approximately arises to the same amplitude in vicinity of the focal point for the two cases, but the post-shock temperature level mainly depends on chemical reactions and molecular dissociations of a gas mixture. While the chemical reaction heat plays an important role in the early stage of detonation wave propagation, gas dissociations dramatically affect the post-shock flow states near the focal point. The maximum pressure and temperature, non-dimensionalized by their initial value, are approximately scaled to the propagation radius over the initial detonation diameter. The post-shock pressure is proportional to the initial pressure of the detonable mixture, and the post-shock temperature is also increased with the initial pressure, but in a much lower rate than that of the post-shock pressure.

An Analytical Solution for Three-Dimensional Diffraction of Plane P-Waves by a Hemispherical Alluvial Valley with Saturated Soil Deposits

An analytical solution for the three-dimensional scattering and diffraction of plane P-waves by a hemispherical alluvial valley with saturated soil deposits is developed by employing Fourier-Bessel series expansion technique. Unlike previous studies, in which the saturated soil deposits were simulated with the single-phase elastic theory, in this paper, they are simulated with Biot's dynamic theory for saturated porous media, and the half space is assumed as a single-phase elastic medium. The effects of the dimensionless frequency, the incidence angle of P-wave and the porosity of soil deposits on the surface displacement magnifications of the hemispherical alluvial valley are investigated. Numerical results show that the existence of a saturated hemispherical alluvial valley has much influence on the surface displacement magnifications. It is more reasonable to simulate soil deposits with Biot's dynamic theory when evaluating the displacement responses of a hemispherical alluvial valley with an incidence of P-waves.

Nonlinear Analysis of Submarine Pipelines During Single Point Lifting

基于管道微单元体平衡建立了海管单点提升的非线性力学模型的控制微分方程组,使用变弧长的无量纲代换将动边界问题化为固定边界的两点边值问题,利用maple环境下编制的两点边值问题的打靶法程序得到了该问题在各个提升阶段的数值解答和在单点提升过程中管道的极限弯矩约为0.71q~{1/3}(EI)~{2/3}。

Identification of Nonlinear Systems Through Time-Frequency Filtering Technique

In the previous paper, a class of nonlinear system is mapped to a so-called skeleton linear model (SLM) based on the joint time-frequency analysis method. Behavior of the nonlinear system may be indicated quantitatively by the variance of the coefficients of SLM versus its response. Using this model we propose an identification method for nonlinear systems based on nonstationary vibration data in this paper. The key technique in the identification procedure is a time-frequency filtering method by which solution of the SLM is extracted from the response data of the corresponding nonlinear system. Two time-frequency filtering methods are discussed here. One is based on the quadratic time-frequency distribution and its inverse transform, the other is based on the quadratic time-frequency distribution and the wavelet transform. Both numerical examples and an experimental application are given to illustrate the validity of the technique.

The Interaction Between Shock Waves and Foam in a Shock Tube

An experimental study and a numerical simulation were conducted to investigate the mechanical and thermodynamic processes involved in the interaction between shock waves and low density foam. The experiment was done in a stainless shock tube (80mm in inner diameter, 10mm in wall thickness and 5360mm in length). The velocities of the incident and reflected compression waves in the foam were measured by using piezo-ceramic pressure sensors. The end-wall peak pressure behind the reflected wave in the foam was measured by using a crystal piezoelectric sensor. It is suggested that the high end-wall pressure may be caused by a rapid contact between the foam and the end-wall surface. Both open-cell and closed-cell foams with different length and density were tested. Through comparing the numerical and experimental end-wall pressure, the permeability coefficients a and 0 are quantitatively determined.

Kramers Escape Rate in Nonlinear Diffusive Media

In this paper, we study nonlinear Kramers problem by investigating overdamped systems ruled by the one-dimensional nonlinear Fokker-Planck equation. We obtain an analytic expression for the Kramers escape rate under quasistationary conditions by employing