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ON nonlinear stability IN NONPARALLEL BOUNDARY LAYER FLOW

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Journal of Hydrodynamics 2004年第3期16卷 301-307页

作者： TANGDeng-bin WANGWei-zhi CollegeofAerospaceEngineering NanjingUniversityofAeronauticsandAstronauticsNanjing210016China

The nonlinear stability problem in nonparallel boundary layer flow fortwo-dimensional disturbances was studied by using a newly presented method called Parabolicstability Equations (PSE). A series of new modes generated by the nonlinear interaction ofdisturbance waves were tabu-lately analyzed, and the Mean Flow Distortion (MFD) was numericallygiven. The computational techniques developed, including the higher-order spectral method and themore effective algebraic mapping, increased greatly the numerical accuracy and the rate ofconvergence. With the predictor-corrector approach in the marching procedure, the normalizationcondition was satisfied, and the stability of numerical calculation could be ensured. With differentinitial amplitudes, the nonlinear stability of disturbance wave was studied. The results ofexamples show good agreement with the data given by the DNS using the full Navier-Stokes equations.

关键词： nonlinear stability boundary layer nonparallel flow parabolic stabilityequations (PSE) harmonic

nonlinear stability of rarefaction waves for a viscous radiative and reactive gas with large initial perturbation

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Science China Mathematics 2021年第12期64卷 2637-2666页

作者： Guiqiong Gong Lin He Yongkai Liao School of Mathematics and Statistics Wuhan UniversityWuhan 430072China Hubei Key Laboratory of Computational Science Wuhan UniversityWuhan 430072China College of Mathematics Sichuan UniversityChengdu 610064China Institute of Applied Physics and Computational Mathematics Beijing 100088China

We investigate the time-asymptotically nonlinear stability of rarefaction waves to the Cauchy problem of a one-dimensional compressible Navier-Stokes type system for a viscous,compressible,radiative and reactive gas,where the constitutive relations for the pressure p,the speci c internal energy e,the speci c volume v,the absolute temperature θ,and the specific entropy s are given by p=Rθv+aθ^(4)/3,e=C_(v)θ+avθ^(4),and s=C_(v)lnθ+4avθ^(3)/3+Rln v with R>0,C_(v)>0 and a>0 being the perfect gas constant,the speci c heat and the radiation constant,*** such a specific gas motion,a somewhat surprising fact is that,generally speaking,the pressure p(v,s)is not a convex function of the specific volume v and the specific entropy *** so,we show in this paper that the rarefaction waves are time-asymptotically stable for large initial perturbation provided that the radiation constant a and the strength of the rarefaction waves are sufficiently *** key point in our analysis is to deduce the positive lower and upper bounds on the specific volume and the absolute temperature,which are uniform with respect to the space and the time variables,but are independent of the radiation constant a.

关键词： viscous radiative and reactive gas rarefaction waves nonlinear stability large initial perturbation

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nonlinear stability OF RAREFACTION WAVES FOR A RATE-TYPE VISCOELASTIC SYSTEM

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Chinese Annals of Mathematics,Series B 1999年第2期20卷 223-232页

作者： HSIAOLING PANRONGHUA InstituteofMathematicsAcademiaSinica Beijing1000800China. ProjectsupportedbytheNationalNaturalScienceFoundationofChina.

The authors study a 3×3 rate-type viscoelastic system, which is a relaxation approximationto a 2×2 quasi-linear hyperbolic system, including the well-known p-system. It is shown thatthe rarefaction waves are nonline... 详细信息

关键词： nonlinear stability Rarefaction waves Relaxation approximation

nonlinear stability of Zonally Symmetric Quasi-geostrophic Flow

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Advances in Atmospheric Sciences 1999年第1期16卷 109-120页

作者：刘永明 Department of Mathematics East China Normal University 200062 Shanghai

By using the conservation laws and the method of variational principle, an improved Arnol′d′s second nonlinear stability theorem for the two-dimensional multilayer quasi-geostrophic model in periodic channel is obta... 详细信息

关键词： nonlinear stability Quasi-geostrophic flow Improved Poincare inequality

nonlinear stability Analysis of the Zonal Flows at Middle and High Latitudes

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Advances in Atmospheric Sciences 1999年第4期16卷 569-580页

作者：穆穆吴永辉唐谟智柳海燕 LASG Institute of Atmospheric Physics Chinese Academy of Sciences 100029 Beijing

An attempt has been made to apply Arnold type nonlinear stability criteria to the diagnostic study of the persistence (stability) or breakdown (instability) of the atmospheric flows. In the case of the blocking high, the cut-off low and the zonal flow, the relationships of the geostrophic stream function versus the potential vorticity of the observed atmosphere are analyzed, which indicates that Arnold second type nonlinear stability theorem is more relevant to the observed atmosphere than the first one. For both the stable and unstable zonal flows, Arnold second type nonlinear stability criteria are applied to the diagnosis. The primary results show that our analyses correspond well to the evolution of the atmospheric motions. The synoptically stable zonal flows satisfy Arnol′d second type nonlinear stability criteria; while the synoptically unstable ones violate the nonlinear stability criteria.

关键词： Zonal flow Quasi-geostrophic nonlinear stability Persistence

nonlinear stability of double-deck reticulated circular shallow spherical shell

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Applied Mathematics and Mechanics(English Edition) 2010年第3期31卷 279-290页

作者：徐加初李勇王璠刘人怀 Institute of Applied Mechanics Jinan University

Based on the variational equation of the nonlinear bending theory of doubledeck reticulated shallow shells, equations of large deflection and boundary conditions for a double-deck reticulated circular shallow spherical shell under a uniformly distributed pressure are derived by using coordinate transformation means and the principle of stationary complementary energy. The characteristic relationship and critical buckling pressure for the shell with two types of boundary conditions are obtained by taking the modified iteration method. Effects of geometrical parameters on the buckling behavior are also discussed.

关键词： double-deck reticulated circular shallow spherical shell nonlinear stability equivalent continuum method modified iteration method stationary complementary energy principle

nonlinear stability OF RAREFACTION WAVES TO THE COMPRESSIBLE NAVIER-STOKES EQUATIONS FOR A REACTING MIXTURE WITH ZERO HEAT CONDUCTIVITY

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Acta Mathematica Scientia 2023年第5期43卷 2179-2203页

作者：彭利双黎勇 Faculty of Science Beijing University of TechnologyBeijing 100124China

In this paper,we study the time-asymptotically nonlinear stability of rarefaction waves for the Cauchy problem of the compressible Navier-Stokes equations for a reacting mixture with zero heat conductivity in one *** the corresponding Riemann problem for the compressible Euler system admits the solutions consisting of rarefaction waves only,it is shown that its Cauchy problem has a unique global solution which tends time-asymptotically towards the rarefaction waves,while the initial perturbation and the strength of rarefaction waves are suitably small.

关键词： rarefaction waves reacting mixture nonlinear stability zero heat conductivity

nonlinear stability FOR EADY'S MODEL

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Applied Mathematics and Mechanics(English Edition) 2005年第2期26卷 200-203页

作者：刘永明邱令存 Department of Mathematics East China Normal University Shanghai 200062 P.R.China

Poincaré type integral inequality plays an important role in the study of nonlinear stability (in the sense of (Arnold's) second theorem) for three-dimensional quasi-geostophic flow. The nonlinear stability of (Eady's) model is one of the most important cases in the application of the method. But the best nonlinear stability criterion obtained so far and the linear stability criterion are not coincident. The two criteria coincide only when the period of the channel is infinite. To fill this gap, the enhanced Poincaré inequality was obtained by considering the additional conservation law of momentum and by rigorous estimate of integral inequality. So the new nonlinear stability criterion was obtained, which shows that for (Eady's) model in the periodic channel, the linear stable implies the nonlinear stable.

关键词： Poincaré inequality (Eady's) model nonlinear stability

nonlinear stability OF TWO-MODE SHOCK PROFILES FOR A RATE-TYPEVISCOELASTIC SYSTEM WITH RELAXATION

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Chinese Annals of Mathematics,Series B 1999年第4期20卷 479-488页

作者： HSIAO LING PAN RONGHUA(Institute of Mathematics, Academia Sinica, Beijing 100080, China)E-mail: hsiaol＠***（Current address: SISSA, via Beirut n. 2-4, 34013, nieste, Italy) Acad Sinica Inst Math Beijing 100080 Peoples R China

The authors study a 3 x 3 rate-type viscoelastic system, which is a relaxation approximation to a 2 x 2 quasi-linear hroerbolic system, including the well-known p-system. The nonlinear stability of two-mode shock wave... 详细信息

关键词： nonlinear stability Two-mode shock profiles Relaxation approximation