NONLINEAR SATURATION OF BAROCLINIC INSTABILITY IN THE GENERALIZED PHILLIPS MODEL(Ⅱ)- THE LOWER BOUND ON THE DISTURBANCE ENERGY AND POTENTIAL ENSTROPHY TO THE NONLINEARLY UNSTABLE BASIC FLOW

ＩｎｔｒｏｄｕｃｔｉｏｎＳｉｎｃｅｔｈｅｐｉｏｎｅｅｒｉｎｇｗｏｒｋｏｎｎｏｎｌｉｎｅａｒｓｔａｂｉｌｉｔｙｏｆｐｌａｎａｒｉｎｃｏｍｐｒｅｓｓｉｂｌｅｓｔｅａｄｙｆｌｏｗｂｙＡｒｎｏｌ’ｄ ,ａｇｒｅａｔｄｅａｌｏｆａｔｔｅｎｔｉｏｎｈａｓｂｅｅｎｐａｉｄｔｏｎｏｎｌｉｎｅａｒｓｔａｂｉｌｉｔｙｏｆｆｌｕｉｄ (ｅｓｐｅｃｉａｌｌｙｇｅｏｐｈｙｓｉｃａｌｆｌｕｉｄ)ｍｏｔｉｏｎ ,ａｎｄｍｕｃｈｐｒｏｇｒｅｓｓｈａｓｂｅｅｎｍａｄｅ.ＡｓｍｅｎｔｉｏｎｅｄｉｎＲｅｆ.[1 ] ,ｉｎｔｈｅｒｅａｌａｔｍｏｓ…     

NONLINEAR SATURATION OF BAROCLINIC INSTABILITY IN THE GENERALIZED PHILLIPS MODEL (Ⅰ) -THE UPPER BOUND ON THE EVOLUTION OF DISTURBANCE TO THE NONLINEARLY UNSTABLE BASIC FLOW

On the basis of the nonlinear stability theorem in the context of Arnol’s second theorem for the generalized Phillips model, nonlinear saturation of baroclinic instability in the generalized Phillips model is investigated. By choosing appropriate artificial stable basic flows, the upper bounds on the disturbance energy and potential enstrophy to the nonlinearly unstable basic flow in the generalized Phillips model are obtained, which are analytic completely and without the limitation of infinitesimal initial disturbance.     

NONLINEAR SATURATION OF BAROCLINIC INSTABILITY IN THE GENERALIZED PHILLIPS MODEL (Ⅰ) -THE UPPER BOUND ON THE EVOLUTION OF DISTURBANCE TO THE NONLINEARLY UNSTABLE BASIC FLOW

ＩｎｔｒｏｄｕｃｔｉｏｎＥｖｅｒｓｉｎｃｅＳｈｅｐｈｅｒｄｈａｓｓｕｇｇｅｓｔｅｄａｎｏｖｅｌｍｅｔｈｏｄｔｏｓｔｕｄｙｎｏｎｌｉｎｅａｒｓａｔｕｒａｔｉｏｎｏｆｂａｒｏｔｒｏｐｉｃａｎｄｂａｒｏｃｌｉｎｉｃｉｎｓｔａｂｉｌｉｔｙ[1- 3],ｍａｎｙａｕｔｈｏｒｓｈａｖｅｍａｄｅｆｕｒｔｈｅｒｒｅｓｅａｒｃｈｏｎｔｈｅｐｒｏｂｌｅｍ .Ｓｈｅｐｈｅｒｄ’ｓｍｅｔｈｏｄｉｓａｓｆｏｌｌｏｗｓ:Ｆｉｒｓｔ,ｃｈｏｏｓｅａｃｌａｓｓｏｆｓｔａｂｌｅｂａｓｉｃｆｌｏｗｓ;ｔｈｅｎ ,ｄｅｃｏｍｐｏｓｅｔｈｅｄｉｓｔ…     

ON THE STABILITY OF DISTORTED LAMINAR FLOW(Ⅰ)—BASIC IDEAS AND THEORY

This paper suggests a hydrodynamic stability theory of distorted laminar flow,andpresents a kind of distortion profile,of mean velocity in parallel shear flow.With suchdistortion profiles,the new theory can be used to investigate the stability behaviour ofparallel shear flow,and thus suggests a new possible approach to instability.     

ON THE STABILITY OF DISTORTED LAMINAR FLOW (I)—BASIC IDEAS AND THEORY

This paper suggests a hydrodynamic stability theory of distorted laminar flow, and presents a kind of distortion profile of mean velocity in parallel shear flow. With such distortion profiles, the new theory can be used to investigate the stability behaviour of parallel shear flow, and thus suggests a new possible approach to instability. The Project Supported by National Natural Science Foundation of China.     

AN APPLICATION OF TOPOLOGICAL METHOD TO ANALYSING THE THREE-DIMENSIONAL FLOW IN CASCADES(Ⅱ)-TOPOLOGICAL ANALYSIS ON THE VECTOR FIELD PATTERNS OF SKINFRICTIONS AND SECTION STREAMLINES

With an application of topological analysis,in this paper the skin-friction line patternson compressor and turbine cascade surfaces are depicted and the streamline patterns of thesecondary flow fields in the cross-section of a curved pipe and a turbine cascade are drawnunder given conditions.In addition the structures of vortices within three-dimensionalviscous flow fields in cascades are analysed.     

NEW POINTS OF VIEW ON THE NONLOCAL FIELD THEORY AND THEIR APPLICATIONS TO THE FRACTURE MECHANICS(Ⅱ)--RE-DISCUSS NONLINEAR CONSTITUTIVE EQUATIONS OF NON-LOCAL THERMOELASTIC BODIES

In this paper, nonlinear constitutive equations are deduced strictly according to the constitutive axioms of rational continuum mechanics. The existing judgments are modified and improved. The results show that the constitutive responses of nonlocal thermoelastic body are related to the curvature and higher order gradient of its material space, and there exists an antisymmetric stress whose average value in the domain occupied by thermoelastic body is equal to zero. The expressions of the antisymmetric stress and the nonlocal residuals are given. The conclusion that the directions of thermal conduction and temperature gradient are consistent is reached. In addition, the objectivity about the nonlocal residuals and the energy conservation law of nonlocal field is discussed briefly, and a formula for calculating the nonlocal residuals of energy changing with rigid motion of the spatial frame of reference is derived. Foundation item: the Natural Science Foundation of Province Jiangshu (BK97063)     

NEW POINTS OF VIEW ON THE NONLOCAL FIELD THEORY AND THEIR APPLICATIONS TO THE FRACTURE MECHANICS(Ⅱ)——RE-DISCUSS NONLINEAR CONSTITUTIVE EQUATIONS OF NONLOCAL THERMOELASTIC BODIES

ＩｎｔｒｏｄｕｃｔｉｏｎＡｓａｇｅｎｅｒａｌｉｚａｔｉｏｎｏｆｔｈｅｃｌａｓｉｃａｌｆｉｅｌｄｔｈｅｏｒｙ,ｎｏｎｌｏｃａｌｆｉｅｌｄｔｈｅｏｒｙｃａｎｂｅｕｓｅｄａｓｔｈｅｔｈｅｏｒｅｔｉｃａｌｂａｓｅｉｎｍａｃｒｏ＿ｍｉｃｒｏｍｅｃｈａｎｉｃｓｂ...     

NUMERICAL INVESTIGATION ON FLOW STABILITY OF RAYLEIGH-B?NARD CONVECTION OF COLD WATER IN A RECTANGULAR CAVITY COOLED AND HEATED SYMMETRICALLY RELATIVE TO THE TEMPERATURE OF DENSITY MAXIMUM

为了解具有密度极值流体瑞利-贝纳德对流特有现象和规律,利用有限容积法对长方体腔内关于密度极值温度对称加热-冷却时冷水瑞利-贝纳德对流的分岔特性进行了三维数值模拟,得到了不同条件下的对流结构型态及其分岔序列,分析了密度极值特性、瑞利数、热边界条件以及宽深比对瑞利-贝纳德对流的影响. 结果表明:具有密度极值冷水瑞利-贝纳德对流系统较常规流体更加稳定,且流动型态及其分岔序列更加复杂;相同瑞利数下多种流型可以稳定共存,各流型在相互转变中存在滞后现象;随着宽深比的增加,流动更易失稳,对流传热能力增强;系统在导热侧壁时比绝热侧壁更加稳定,对流传热能力有所减弱;基于计算结果,采用线性回归方法,得到了热壁传热关联式.     

FINITE ELEMENT DISPLACEMENT PERTURBATION METHOD FOR GEOMETRIC NONLINEAR BEHAVIORS OF SHELLS OF REVOLUTION OVERALL BEDING IN A MERIDIONAL PLANE AND APPLICATION TO BELLOW (Ⅱ)

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｅｑｕａｔｉｏｎｓａｎｄｔｈｅｓｏｌｕｔｉｏｎｐｒｏｃｅｄｕｒｅｓｏｆｔｈｅｆｉｎｉｔｅ＿ｅｌｅｍｅｎｔ＿ｄｉｓｐｌａｃｅｍｅｎｔ＿ｐｅｒｔｕｒｂａｔｉｏｎｍｅｔｈｏｄ (ＦＥＤＰＭ)ｆｏｒｔｈｅｇｅｏｍｅｔｒｉｃｎｏｎｌｉｎｅａｒｂｅｈａｖｉｏｒｓｏｆｓｈｅｌｌｓｏｆｒｅｖｏｌｕｔｉｏｎｓｕｂｊｅｃｔｅｄｔｏｐｕｒｅｂｅｎｄｉｎｇｍｏｍｅｎｔｓｏｒｌａｔｅｒａｌｆｏｒｃｅｓｉｎｏｎｅｏｆｔｈｅｉｒｍｅｒｉｄｉｏｎａｌｐｌａｎｅｓｗｅｒｅｐｒｅｓｅｎｔｅｄｉｎ (Ⅰ ) .…     

FINITE ELEMENT DISPLACEMENT PERTURBATION METHOD FOR GEOMETRIC NONLINEAR BEHAVIORS OF SHELLS OF REVOLUTION OVERALL BEDING IN A MERIDIONAL PLANE AND APPLICATION TO BELLOW (Ⅱ)

The finite-element-displacement-perturbation method (FEDPM)for the geometric nonlinear behaviors of shells of revolution subjected to pure bending moments or lateral forces in one of their meridional planes (Ⅰ) was employed to calculate the stress distributions and the stiffness of the bellows. Firstly, by applying the first-order perturbation solution (the linear solution)of the FEDPM to the bellows, the obtained results were compared with those of the general solution and the initial parameter integration solution proposed by the present authors earlier, as well as of the experiments and the FEA by others.It is shown that the FEDPM is with good precision and reliability, and as it was pointed out in (Ⅰ) the abrupt changes of the meridian curvature of bellows would not affect the use of the usual straight element. Then the nonlinear behaviors of the bellows were discussed. As expected, the nonlinear effects mainly come from the bellows ring plate,and the wider the ring plate is, the stronger the nonlinear effects are. Contrarily, the vanishing of the ring plate, like the C-shaped bellows, the nonlinear effects almost vanish. In addition, when the pure bending moments act on the bellows, each convolution has the same stress distributions calculated by the linear solution and other linear theories, but by the present nonlinear solution they vary with respect to the convolutions of the bellows. Yet for most bellows, the linear solutions are valid in practice.