The Perturbed Problem on the Boussinesq System of Rayleigh-Bénard Convection

In this paper,the infinite Prandtl number limit of Rayleigh-B′enard convection is studied.For well prepared initial data,the convergence of solutions in L∞(0,t;H2(G)) is rigorously justified by analysis of asymptotic expansions.     

Well-posedness for compressible Rayleigh-Bénard convection

The Rayleigh-B~nard convection is a classical problem in fluid dynamics. In this paper, we are concerned with the well-posedness for the compressible Rayleigh-B~nard convection in a bounded domain Ω R2. We prove the local well-posedness of the system with appropriate initial data. This is the result concerning compressible Rayleigh-B~nard convection, before only results about incompressible Rayleigh-B~nard convection were done.     

Rayleigh-Bénard对流的Boussinesq系统奇异摄动问题

运用奇异摄动理论的渐进展开法和能量方法,研究了Rayleigh-Benard对流的Boussinesq近似系统的奇异摄动问题,得到了Boussinesq近似系统结构明确的渐进近似解,在L2空间中判断了收敛,其收敛率分别为o(ε1÷2),o(ε)(最优收敛率).     

Modeling of Free Convection Boundary Layer Flow on a Solid Sphere with Newtonian Heating

In this paper, the mathematical model of free convection boundary layer flow on a solid sphere with Newtonian heating, in which the heat transfer from the surface is proportional to the local surface temperature, is considered. The transformed boundary layer equations are solved numerically using an efficient numerical scheme known as the Keller-box method. Numerical solutions are obtained for the local wall temperature, the local skin friction coefficient, as well as the velocity and temperature profiles. The features of the flow and heat transfer characteristics for different values of the Prandtl number Pr and conjugate parameter γ are analyzed and discussed.     

用子波方法研究Rayleigh-Bénard对流温度信号的标度律

采用子波分析方法 ,对实验中测得的Rayleigh_B啨ｎａｒｄ对流温度信号 (被动标量 )的标度律 ,从以下两个方面进行了研究 :第一方面 ,直接采用扩展的结构函数 (ESS)的公式对温度信号进行了分析 ,研究结果表明 ,采用该方法后的标度区域明显比不采用扩展结构函数的标度区域要宽 ,得到的标度指数与其它实验中得到的温度信号标度指数 ξ(q)一致 ;第二个方面 ,将 A .Arneodo等人对湍流中速度信号提出的基于子波分析的扩展标度公式 ,推广应用于温度信号 ,给出了一个描述温度信号的、基于子波分析的扩展标度公式 ,研究结果表明 ,提出的建立在子波系数极大模求和基础上的扩展标度公式 ,也能够比较准确地提取温度信号的标度指数 ξ(q) ·     

The limit of the Boussinesq system of Rayleigh-Bénard convection as the Prandtl number approaches infinity

In this paper, the initial layer problem and infinite Prandtl number limit of Rayleigh-Bénard convection is studied by the asymptotic expansion methods of singular perturbation theory and the classical energy methods. For ill-prepared initial data, an exact approximating solution with expansions up to any order are given and the convergence rates O(ɛ ^m+1/2) and the optimal convergence rates O(ɛ ^m+1) are obtained respectively. This improves the result of J.G. SHI.     

Global Well-posedness for the 2D Micropolar Rayleigh–Bénard Convection Problem without Velocity Dissipation

In this article, we study the Cauchy problem to the micropolar Rayleigh–Bénard convection problem without velocity dissipation in two dimension. We first prove the local well-posedness of a smooth solution, and then establish a blow up criterion in terms of the gradient of scalar temperature field. At last, we obtain the global well-posedness to the system.     

Boundary layers associated with the 3-D Boussinesq system for Rayleigh–Bénard convection

We investigate the boundary layer effects of the 3-D incompressible Boussinesq system for Rayleigh–Bénard convection with vanishing diffusivity limit. By adopting the multi-scale analysis and the asymptotic expansion methods of singular perturbation theory, we construct an exact approximating solution for the viscous and diffusive Boussinesq system with well-prepared initial data. In addition, we obtain the convergence result of the vanishing diffusivity limit.     

Loss of stability in the magnetic Bénard problem

Received January 1999; Revised April 1999     

Two Limit Cycles in Liénard Piecewise Linear Differential Systems

Some techniques for studying the existence of limit cycles for smooth differential systems are extended to continuous piecewise linear differential systems. Rigorous new results are provided on the existence of two limit cycles surrounding the equilibrium point at the origin for systems with three zones separated by two parallel straight lines without symmetry. As a relevant application, it is shown the existence of bistable regimes in an asymmetric memristor-based electronic oscillator.

     

Numerical simulation of solutal Rayleigh-Bénard-Marangoni convection in a layered two-phase system

We present a two-dimensional simulation of solutal Rayleigh-Bénard-Maragoni convection in a layered system. In the initial state, the solute concentration is homogeneous in each layer but not in partition equilibrium. Diffusive transfer of solute leads to convective instability. Marangoni convection dominates initially as it operates on a smaller length scale. Rayleigh convection appears later as an instability of the mixed unstably stratified fluid near the interface. Compared to pure Marangoni convection the dynamics is more disordered due to additional flow in the bulk. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The effect of suspended particles on Rayleigh-Bénard convection I. A nonlinear stability analysis of a thermal equilibrium model

The weakly nonlinear stability of the pure conduction solution for an appropriate aerosol one-layer Rayleigh-Bénard model of a Boussinesq particle-gas system in thermal equilibrium which retains both the particle and collision pressures is investigated. The main result of this analysis is in qualitative accord with the dominant but heretofore anomalous characteristic of columnar instabilities observed in smoke-air mixtures: namely, that lowering the threshold temperature gradient associated with the occurrence of the supercritically equilibrated rolls predicted for a clean gas leads to reduction increasing with decreasing layer depth which becomes quite severe in the case of very thin layers.     

On one conjecture in the theory of isochronous Liénard systems

New normal forms are obtained for the center as well as isochronous center of holomorphic Liénard systems.     

The effect of suspended particles on Rayleigh-Bénard convection II. A nonlinear stability analysis of a thermal disequilibrium model

The weakly nonlinear stability of the pure conduction solution for an appropriate aerosol one-layer Rayleigh-Bénard model of a Boussinesq particle-gas system retaining both the particle and collision pressures and considering particle to particle radiative effects while relaxing the usual assumption of thermal equilibrium between those particles and the gas is investigated. Then an analysis of the criteria governing the occurrence of supercritically re-equilibrated stationary rolls yields a minimum Rayleigh number and a critical wavelength which are completely compatible in their layer-depth behavior with normal convective and columnar instabilities observed in mixtures of smoke with air or carbon dioxide.     

The Mathematical Model and Research Progress of the Boundary Layer Flashback in Premixed Combustion北大核心CSCD

Flashback is a key problem influencing the normal operation of power equipment such as gas turbines. As one of the main mechanisms that cause flashback, the boundary layer flashback has an important effect on the design and operation of gas turbine combustors and other combustion devices. Since the critical gradient model for the boundary layer flashback was put forward by Lewis et al. in 1945, the theoretical models for the boundary layer flashback, such as the Peclet number model, the Damköhler number model and the flame angle theory, were developed one after another. However, these theoretical models still need improvements. Until now, the theoretical models for the boundary layer flashback are still in continuous development and modification. The history of the boundary layer flashback was reviewed, and the background, pertinence and shortcomings of the theoretical models were elucidated in the order of the model establishment time. In addition, the development status and research progress of the theoretical models for the boundary layer flashback in recent years were summarized, especially the progress made with new methods such as numerical simulation and statistical analysis. Further, the theoretical research direction and breakthrough points of the combustion boundary layer flashback at present and in the future were put forward. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.