Orbital Stability of Solitary Waves for Generalized Zakharov System

In the interaction of laser-plasma the system of Zakharov equation plays an important role.This system attracted many scientists' wide interest and attention.And the formation, evolution and interaction of the Langmuir solutions differ from solutions of the KDV equation. Here we consider the following generalized Zakharov

THE STABILITY OF THE DELTA WAVE TO PRESSURELESS EULER EQUATIONS WITH VISCOUS AND FLUX PERTURBATIONS

This paper is concerned with the pressureless Euler equations with viscous and flux perturbations.The existence of Riemann solutions to the pressureless Euler equations with viscous and flux perturbations is obtained.We show the stability of the delta wave of the pressureless Euler equations to the perturbations;that is,the limit solution of the pressureless Euler equations with viscous and flux perturbations is the delta wave solution of the pressureless Euler equations as the viscous and flux perturbation simultaneously vanish in the case u_(-)> u_(+).

Nolinear waves and their barotropic stability in the tropical ocean and atmosphere

In this paper, the nonlinear waves and their barotropic stability in the tropical ocean and atmosphere are studied with the qualitative theory of the ordinary differential equation. The relationship is derived between the stability of nonlinear waves with different frequencies and the basic currents and their horizontal shear in the tropical ocean and atmosphere.

EXISTENCE AND STABILITY OF VISCOUS SHOCK PROFILES FOR 2-D ISENTROPIC MHD WITH INFINITE ELECTRICAL RESISTIVITY

For the two-dimensional Navier-Stokes equations of isentropic magnetohydrodynamics （MHD） with γ-law gas equation of state, γ≥ 1, and infinite electrical resistivity, we carry out a global analysis categorizing all possible viscous shock profiles. Precisely, we show that the phase portrait of the traveling-wave ODE generically consists of either two rest points connected by a viscous Lax profile, or else four rest points, two saddles and two nodes. In the latter configuration, which rest points are connected by profiles depends on the ratio of viscosities, and can involve Lax, overcompressive, or undercompressive shock profiles. Considered as three-dimensional solutions, undercompressive shocks axe Lax-type （Alfven） waves. For the monatomic and diatomic cases γ= 5/3 and γ=7/5, with standard viscosity ratio for a nonmagnetic gas, we find numerically that the the nodes are connected by a family of overcompressive profiles bounded by Lax profiles connecting saddles to nodes, with no undercompressive shocks occurring. We carry out a systematic numerical Evans function analysis indicating that all of these two-dimensional shock pro- files are linearly and nonlinearly stable, both with respect to two- and three-dimensional perturbations. For the same gas constants, but different viscosity ratios, we investigate also cases for which undercompressive shocks appear; these are seen numerically to be stable as well, both with respect to two-dimensional and （in the neutral sense of convergence to nearby Riemann solutions） three-dimensional perturbations.

Dynamic Stability Analysis of Caisson Breakwater in Lifetime Considering the Annual Frequency of Severe Storm

In the dynamic stability analysis of a caisson breakwater, most of current studies pay attention to the motion characteristics of caisson breakwaters under a single periodical breaking wave excitation. And in the lifetime stability analysis of caisson breakwater, it is assumed that the caisson breakwater suffers storm wave excitation once annually in the design lifetime. However, the number of annual severe storm occurrence is a random variable. In this paper, a series of random waves are generated by the Wen Sheng-chang wave spectrum, and the histories of successive and long-term random wave forces are built up by using the improved Goda wave force model. It is assumed that the number of annual severe storm occurrence is in the Poisson distribution over the 50-year design lifetime, and the history of random wave excitation is generated for each storm by the wave spectrum. The response histories of the caisson breakwater to the random waves over 50-year design lifetime are calculated and taken as a set of samples. On the basis of the Monte Carlo simulation technique, a large number of samples can be obtained, and the probability assessment of the safety of the breakwater during the complete design lifetime is obtained by statistical analysis of a large number of samples. Finally, the procedure of probability assessment of the breakwater safety is illustrated by an example.

不同装载条件下小型渔船参数横摇的非定常RANS CFD仿真

Fishing boats have unique features that make them prone to changing loading conditions.When the boat leaves the port,the empty fish tank gradually fills up during fishing operations which may result in parametric roll(PR).This dangerous phenomenon that can lead to capsizing.The present study aims to understand better the behaviour of parametric roll in fishing boats and its relation to changing loading conditions.The study considers the effects of displacement and the GM/KM ratio on parametric roll,as well as the longitudinal flare distribution at the waterline.Two assessments to detect the parametric roll occurrence in early stage were carried out by using the level 1 assessment of parametric roll based on the Second Generation of Intact Stability criteria(SGIS)from International maritime Organisation(IMO)and the Susceptibility criteria of Parametric roll from the American Bureau of Shipping(ABS).Then,the CFD method is used to predict the amplitude of the parametric roll phenomenon.The results provide important insights to fishing vessel operators on how to manage loading conditions to maintain stability and avoid hazardous situations.By following the guidelines outlined in this study,fishing boats can operate more safely and efficiently,reducing the risk of accidents and improving the overall sustainability of the fishing industry.

Stability of Rarefaction Wave for Compressible Navier-Stokes Equations on the Half Line

This paper is concerned with the large-time behavior of solutions to an initial-boundary-value problem for full compressible Navier-Stokes equations on the half line（0,∞）,which is named impermeable wall problem.It is shown that the 3-rarefaction wave is stable under partially large initial perturbation if the adiabatic exponent γ is close to 1.Here partially large initial perturbation means that the perturbation of absolute temperature is small,while the perturbations of specific volume and velocity can be large.The proof is given by the elementary energy method.

Stability/Instability of Solitary waves with Nonzero Asymptotic Value for a PDE in Microstructural Solid Materials

The present paper deals with results of stability/instability of solitary waves with nonzero asymptotic value for a microstructure PDE. By the exact solitary wave solutions and detailed computations, we set up the explicit expression for the discrimination d′′（c）. Finally, a complete study of orbital stablity/instablity for the explicit exact solutions is given.

TRAVELING WAVE SOLUTIONS AND THEIR STABILITY OF NONLINEAR SCHRDINGER EQUATION WITH WEAK DISSIPATION

In this paper,several new constant-amplitude and variable-amplitude wave solutions（namely,traveling wave solutions） of a generalized nonlinear Schrdinger equation are investigated by using the extended homogeneous balance method,where the balance method is applied to solve the Riccati equation and the reduced nonlinear ordinary differential equation,respectively.In addition,stability analysis of those solutions are also conducted by regular phase plane technique.

The influence of wave surge force on surf-riding/broaching vulnerability criteria check

This study focuses on the influence of the wave surge force on the assessments of the surf-riding/broaching vulnerability criteria according to the new proposal of the IMO Second Generation Intact Stability Criteria. A code is developed for the criteria check and the sample ship calculations show that the accuracy of the wave surge force estimation has a significant influence on the assessment result. For further investigation, the wave surge force measurement through a captive model test is made for a purse seiner to validate the numerical model, the effects of the wave steepness and the ship forward speed on the wave surge force responses are also discussed. It is demonstrated that the diffraction effect is important for the correct estimation of the wave surge force. Therefore, it is recommended to include this effect in the assessment procedure.

Analysis of shock wave reflection from fixed and moving boundaries using a stabilized particle method

In the present paper, the efficiency of an enhanced formulation of the stabilized corrective smoothed particle method （CSPM） for simulation of shock wave propagation and reflection from fixed and moving solid boundaries in compressible fluids is investigated. The Lagrangian nature and its accuracy for imposing the boundary conditions are the two main reasons for adoption of CSPM. The governing equations are further modified for imposition of moving solid boundary conditions. In addition to the traditional artificial viscosity, which can remove numerically induced abnormal jumps in the field values, a velocity field smoothing technique is introduced as an efficient method for stabilizing the solution. The method has been implemented for one- and two-dimensional shock wave propagation and reflection from fixed and moving boundaries and the results have been compared with other available solutions. The method has also been adopted for simulation of shock wave propagation and reflection from infinite and finite solid boundaries.