THE LOW MACH NUMBER LIMIT FOR ISENTROPIC COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH A REVISED MAXWELL'S LAW

We investigate the low Mach number limit for the isentropic compressible NavierStokes equations with a revised Maxwell's law(with Galilean invariance) in R^(3). By applying the uniform estimates of the error system, it is proven that the solutions of the isentropic Navier-Stokes equations with a revised Maxwell's law converge to that of the incompressible Navier-Stokes equations as the Mach number tends to zero. Moreover, the convergence rates are also obtained.

POINTWISE ESTIMATE OF SOLUTIONS OF ISENTROPIC NMIER-STOKES EQUATIONS IN EVEN SPACE-DIMENSION

This paper is concerned with the dissipation of solutions of the isentropic Navier-Stokes equations in even and bigger than two multi-dimensions. Pointwise estimates of the time-asymptotic shape of the solutions are obtained and the generalized Huygan's principle is exhibited. The approch of the paper is based on the detailed analysis of the Green function of Iinearized system. This is used to study the coupling of nonlinear diffesion waves.

GLOBAL EXISTENCE OF STRONG SOLUTIONS OF NAVIER-STOKES EQUATIONS WITH NON-NEWTONIAN POTENTIAL FOR ONE-DIMENSIONAL ISENTROPIC COMPRESSIBLE FLUIDS

The aims of this paper are to discuss global existence and uniqueness of strong solution for a class of isentropic compressible navier-Stokes equations with non-Newtonian in one-dimensional bounded intervals. We prove two global existence results on strong solutions of isentropic compressible Navier-Stokes equations. The first result shows only the existence. And the second one shows the existence and uniqueness result based on the first result, but the uniqueness requires some compatibility condition.

TIME-PERIODIC ISENTROPIC SUPERSONIC EULER FLOWS IN ONE-DIMENSIONAL DUCTS DRIVING BY PERIODIC BOUNDARY CONDITIONS

We show existence of time-periodic supersonic solutions in a finite interval, after certain start-up time depending on the length of the interval, to the one space-dimensional isentropic compressible Euler equations, subjected to periodic boundary conditions. Both classical solutions and weak entropy solutions, as well as high-frequency limiting behavior are considered. The proofs depend on the theory of Cauchy problems of genuinely nonlinear hyperbolic systems of conservation laws.

GLOBAL L~∞ SOLUTIONS TO SYSTEM OF ISENTROPIC GAS DYNAMICS IN A DIVERGENT NOZZLE WITH FRICTION

In this article, we study the global L^∞ entropy solutions for the Cauchy problem of system of isentropic gas dynamics in a divergent nozzle with a friction. Especially when the adiabatic exponent γ=3, we apply for the maximum principle to obtain the L^∞ estimates w(ρ^δ,ε, u^δ,ε)≤ B(t) and z(ρ^δ,ε, u^δ,ε)≤ B(t) for the viscosity solutions (ρ^δ,ε, u^δ,ε), where B(t) is a nonnegative bounded function for any finite time t. This work, in the special case γ≥ 3, extends the previous works, which provided the global entropy solutions for the same Cauchy problem with the restriction w(ρ^δ,ε, u^δ,ε)≤ 0 or z(ρ^δ,ε, u^δ,ε)≤ 0.

An Isentropic Mass Circulation View on the Extreme Cold Events in the 2020/21 Winter

Three extreme cold events successively occurred across East Asia and North America in the 2020/21 winter.This study investigates the underlying mechanisms of these record-breaking persistent cold events from the isentropic mass circulation(IMC)perspective.Results show that the midlatitude cold surface temperature anomalies always co-occurred with the high-latitude warm anomalies,and this was closely related to the strengthening of the low-level equatorward cold air branch of the IMC,particularly along the climatological cold air routes over East Asia and North America.Specifically,the two cold surges over East Asia in early winter were results of intensification of cold air transport there,influenced by the Arctic sea ice loss in autumn.The weakened cold air transport over North America associated with warmer northeastern Pacific sea surface temperatures(SSTs)explained the concurrent anomalous warmth there.This enhanced a wavenumber-1 pattern and upward wave propagation,inducing a simultaneous and long-lasting stronger poleward warm air branch(WB)of the IMC in the stratosphere and hence a displacement-type Stratospheric Sudden Warming(SSW)event on 4 January.The WB-induced increase in the air mass transported into the polar stratosphere was followed by intensification of the equatorward cold branch,hence promoting the occurrence of two extreme cold events respectively over East Asia in the beginning of January and over North America in February.Results do not yield a robust direct linkage from La Niña to the SSW event,IMC changes,and cold events,though the extratropical warm SSTs are found to contribute to the February cold surge in North America.

CONVERGENCE OF THE LAX-FRIEDRICHS SCHEME FOR ISENTROPIC GAS DYNAMICS (Ⅰ)

A compactness frame of the Lax-Friedrichs scheme for the equations of gas dynamics is obtained by using some embedding theorems and an analysis of the difference scheme and the weak entropy.

GLOBAL ENTROPY SOLUTIONS TO AN INHOMOGENEOUS ISENTROPIC COMPRESSIBLE EULER SYSTEM

In this article, we develop a new technique to prove the global existene of entropy solutions to an inhomogeneous isentropic compressible Euler equations through the compensated compactness and vanishing viscosity method. In particular, the entropy solutions are uniformly bounded independent of time.

Is the Isentropic Surface Always Impermeable to the Potential Vorticity Substance?

The impermeability of isentropic surfaces by the potential vorticity substance （PVS） has often been used to help understand the generation of potential vorticity in the presence of diabatic heating and friction. In this study, we examined singularities of isentropic surfaces that may develop in the presence of diabatic heating and the fictitious movements of the isentropic surfaces that are involved in deriving the PVS impermeability theorem. Our results show that such singularities could occur in the upper troposphere as a result of intense convective-scale motion, at the cloud top due to radiative cooling, or within the well-mixed boundary layer. These locally ill-defined conditions allow PVS to penetrate across an isentropic surface. We conclude that the PVS impermeability theorem is generally valid for the stably stratified atmosphere in the absence of diabatic heating.

A SUPPLEMENT TO THE PAPERS CONVERGENCE OF THE LAX-FRIEDRICHS SCHEME FOR ISENTROPIC GAS DYNAMICS (Ⅱ)-(Ⅲ)

In the papers (Ⅱ)—(Ⅲ), we studied the global existence of the solutions for the isentropic equation of gas dynamics

The Development and Initial Tests of an Atmospheric Model Based on a Vertical Coordinate with a Smooth Transition from Terrain Following to Isentropic Coordinates

An atmospheric model (η model) is developed by modifying the UW θ-σ hybrid model. In the η model, the vertical coordinate transforms smoothly from terrain following to isentropic coordinates. The model is developed to capitalize on the inherent advantage of numerical modeling in isentropic coordinates and to eliminate the interface between the sigma planetary boundary layer and isentropic free atmosphere present in the UW θ-σ model. This formulation provides the potential for the data assimilation and the application of higher order schemes. This paper describes the structure of the η model and presents results from initial numerical experiments. The first experiment tests the capability of the η model for simulating the baroclinic development process. In the 48-hr numerical weather forecast experiment, the η model produces reasonable precipitation and synoptic fields at all levels which are similar to those from the UW θ-σ model. The second and third experiments test the capability of the η model for conserving 1) the joint distribution of isentropic potential vorticity (IPV) and proxy ozone and 2) equivalent potential temperature under frictionless and isentropic conditions. These experiments show that distributions of IPV and proxy ozone in the pure isentropic domain and the distributions of prognostic and diagnostic equivalent potential temperture in the model domain remain highly correlated to day 10.

CAUCHY PROBLEM FOR LINEARIZED SYSTEM OF TWO-DIMENSIONAL ISENTROPIC FLOW WITH AXISYMMETRICAL INITIAL DATA IN GAS DYNAMICS

The explicit solution to Cauchy problem for linearized system of two-dimensional isentropic flow with axisymmetrical initial data in gas dynamics is given.

The Isentropic Exponent of Single-Ionized Mono-Atomic Plasmas

The isentropic exponent of single-ionized mono-atomic plasmas in thermal equilib- rium is studied. Its behavior as a function of the ionization degree and temperature is examined for argon and zinc plasmas at two pressures （1 bar and 1 mbar, 1 mPa and 1 Pa）, respectively. The results show that for the two sorts of plasma the isentropic exponent equals typically about 1.1-1.2 within a considerably wide range of the ionization degree （5%-80%）.

ENTROPY CONSISTENCY OF LARGE TIME STEP SCHEMES FOR ISENTROPIC EQUATIONS OF GAS DYNAMICS

In this paper, We show for isentropic equations of gas dynamics with adiabatic exponent gamma=3 that approximations of weak solutions generated by large time step Godunov's scheme or Glimm's scheme give entropy solution in the limit if Courant number is less than or equal to 1.

CONVERGENCE OF THE APPROXIMATE SOLUTIONS TO ISENTROPIC GAS DYNAMICS

This paper gives four pairs of entropies (η_i, q_i) (i=1, 2, 3, 4) to the isentropic gas dynamics equations ρ_t+(ρu)_x=0 (ρu)_t+(ρu^2+p(ρ))_x=0 p(ρ)=k^2ρ~γ,1<γ<3。 when all the function equations are satisfied

Ultrasonic, Volumetric and Isentropic Compressibility of Binary Mixtures of 1,4-Dioxane with Primary Alcohols at 303.15 K

Density, viscosity and sound velocity of six binary liquid mixtures of methanol, ethanol, propanol, butanol, hexanol and octanol with 1,4-dioxane have been measured over the entire range of composition at temperature 303.15K. From the experimental densities, viscosities and sound velocity, the excess molar volume (VE), deviation in viscosity (Δη) and deviation in isentropic compressibility (ΔKS) have been calculated. The results have been used to discuss the nature and strength of intermolecular interactions in these mixtures.

A Method for Determining the Operable Ideal Condensation Temperature of Dry and Isentropic Fluids Used in Organic Rankine Cycle(ORC)Based on Temperature-Entropy(T-s)Diagram

Condensation temperature is one of the crucial parameters determining the performance of an organic Rankine cycle.It is necessary to consider the differences in the working fluids themselves when setting the condensation temperature of organic Rankine cycle.In current study,temperature-entropy(T-s)diagram is employed to describe the difference in working fluids.Three areas of dry and isentropic fluids in a temperature-entropy(T-s)diagram,which are the area denoting net output work of cycle(A_(1),the area denoting net output work of the Carnot cycle(A),and the curved triangle in superheated region denoting condensation characteristics(A_(2)),are defined.On this basis,the ratio of A_(2)to A_(1)and the ratio of A_(1)to A are calculated.Logarithmic Mean Difference of the above two ratios is obtained to determine the operable ideal condensation temperature of 66 dry and isentropic fluids employed in Organic Rankine Cycle.The findings indicate that the operable ideal condensation temperatures for the majority of dry and isentropic fluids are in the range of 305 K to 310 K.The work presented in this study may be useful for designing and establishing an Organic Rankine Cycle system.

Analysis of Isentropic Potential Vorticity for a Strong Cold Wave During 2004/2005 Winter

Using the NCAR/NCEP daily reanalysis data from 1 December 2004 to 28 February 2005, the isentropic potential vorticity （IPV） analysis of a strong cold wave from 22 December 2004 to 1 January 2005 was made. It is found that the strong cold air of the cold wave originated from the lower stratosphere and upper troposphere of the high latitude in the Eurasian continent and the Arctic area. Before the outbreak of the cold wave, the strong cold air of high PV propagated down to the south of Lake Baikal, and was cut off by a low PV air of low latitude origin, forming a dipole-type circulation pattern with the low PV center （blocking high） in the northern Eurasian continent and the high PV one （low vortex） in the southern part. Along with decaying of the low PV center, the high PV center （strong cold air） moved towards the southeast along the northern flank of the Tibetan Plateau. When it arrived in East China, the air column of high PV rapidly stretched downward, leading to increase in its cyclonic vorticity, which made the East Asian major trough to deepen rapidly, and finally induced the outbreak of the cold wave. Further analysis indicates that in the southward and downward propagation process of the high PV center, the air flow west and north of the high PV center on isentropic surface subsided along the isentropic surface, resulting in rapid development of Siberian high, finally leading to the southward outbreak of the strong cold wave.

Elementary Waves of Two-dimensional Steady Isentropic Flow

A self similar solution is developed for two dimensional, steady, isentropic and inviscid flow. Some fundamental properties are clarified for centered simple waves R and shock waves S. The present paper provides further theoretical analysis to clarify the results obtained by Glimm et al. using theoretical and computational methods.

ISENTROPIC POTENTIAL VORTICITY ANALYSIS ON THE MESOSCALE CYCLONE DEVELOPMENT IN A TORRENTIAL RAIN PROCESS

The mesoscale model MM4 is used to simulate the torrential rain associated with Meiyu front occurring on 5—6 July.1991 in the Changjiang-Huaihe Basin.Based on the outputs of the model, the cause of the mesoscale cyclogenesis on the lower troposphere is investigated in terms of the potential vorticity principle.The results show that because of the favorable pattern of moist isentropic surface,the absolute vorticity increases when cold air with high moist potential vorticity value rapidly slides down southwards along the moist isentropic surface,and then causes the cyclonic vortex development.