By using NCAR/NCEP daily reanalysis data and the precipitation data in Liaoning routine automatic station during July 14-16,2008,the regional rainstorm weather process in Liaoning was done the isentropic analysis. Acc...By using NCAR/NCEP daily reanalysis data and the precipitation data in Liaoning routine automatic station during July 14-16,2008,the regional rainstorm weather process in Liaoning was done the isentropic analysis. According to the variation characteristics of isobar,isocratic specific humidity line and wind field on the isentropic surface,the rainstorm landing zone was gained and compared with the analysis results of isobaric surface. The results showed that the warm wet transportation belt on 330 K isentropic surface provided the rich water vapor condition for the rainstorm generation,and the distribution of air-pressure and wind field on the isentropic surface favored to understand the movement of airflow. Compared with the analysis of isobaric surface,the analysis of isobaric surface could better directly judge the landing zone of precipitation,and the forecast effect was better than the analysis forecast results of isobaric surface.展开更多
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 o...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.展开更多
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 isent...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.展开更多
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...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.展开更多
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, ...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.展开更多
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 ...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.展开更多
Speed of sound data for butyl acetate＋benzene, or toluene, or o-xylene, or m-xylene, or p-xylene binary mixtures have been measured over the entire range of mole fraction at 308.15 K. The excess isentropic compressib...Speed of sound data for butyl acetate＋benzene, or toluene, or o-xylene, or m-xylene, or p-xylene binary mixtures have been measured over the entire range of mole fraction at 308.15 K. The excess isentropic compressibilities （ Ks^E ） were computed from speed of sound and density data, derived from molar excess volume data. The Ks^E values were analyzed by using graph theoretical approach. The Ks^E values evaluated by graph theory compared reasonably well with their corresponding experimental values. The Ks^E data were also expressed in terms of Redlich-Kister polynomial equation to derive the coefficients and the standard deviation.展开更多
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.
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 met...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.展开更多
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 ...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.展开更多
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 syste...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.展开更多
The paper concerns with generalized Riemann problem for isentropic flow with dissipation, and show that if the similarity solution to Riemann problem is composed of a backward centered rarefaction wave and a forward c...The paper concerns with generalized Riemann problem for isentropic flow with dissipation, and show that if the similarity solution to Riemann problem is composed of a backward centered rarefaction wave and a forward centered rarefaction wave, then generalized Riemann problem admits a unique global solution on t≥0. This solution is composed of backward centered wave and a forward centered wave with the origin as their center and then continuous for t 〉0.展开更多
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 develope...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.展开更多
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 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 pres...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%）.展开更多
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 entrop...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.展开更多
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 s...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展开更多
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 ...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 (<i>V<sup>E</sup></i>), deviation in viscosity (Δ<i>η</i>) and deviation in isentropic compressibility (Δ<i>K<sub>S</sub></i>) have been calculated. The results have been used to discuss the nature and strength of intermolecular interactions in these mixtures.展开更多
The author studies the 2D isentropic Euler equations with the ideal gas law.He exhibits a set of smooth initial data that give rise to shock formation at a single point near the planar symmetry.These solutions to the ...The author studies the 2D isentropic Euler equations with the ideal gas law.He exhibits a set of smooth initial data that give rise to shock formation at a single point near the planar symmetry.These solutions to the 2D isentropic Euler equations are associated with non-zero vorticity at the shock and have uniform-in-time-1/3-Holder bound.Moreover,these point shocks are of self-similar type and share the same profile,which is a solution to the 2D self-similar Burgers equation.The proof of the solutions,following the 3D construction of Buckmaster,Shkoller and Vicol(in 2023),is based on the stable 2D self-similar Burgers profile and the modulation method.展开更多
文摘By using NCAR/NCEP daily reanalysis data and the precipitation data in Liaoning routine automatic station during July 14-16,2008,the regional rainstorm weather process in Liaoning was done the isentropic analysis. According to the variation characteristics of isobar,isocratic specific humidity line and wind field on the isentropic surface,the rainstorm landing zone was gained and compared with the analysis results of isobaric surface. The results showed that the warm wet transportation belt on 330 K isentropic surface provided the rich water vapor condition for the rainstorm generation,and the distribution of air-pressure and wind field on the isentropic surface favored to understand the movement of airflow. Compared with the analysis of isobaric surface,the analysis of isobaric surface could better directly judge the landing zone of precipitation,and the forecast effect was better than the analysis forecast results of isobaric surface.
基金Supported in part by National Natural Science Foundationof China (19871065) Hua-Cheng Grant
文摘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.
基金supported by grants from the National Key R&D Program of China(Grant No.2019YFC1510201)National Natural Science Foundation of China(Grant Nos.42075052 and 42088101)the Natural Science Foundation of Jiangsu Province(Grants No.BK20211288).
文摘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.
文摘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.
基金supported by the National Natural Science Foundation of China(11371141 and 11871218)Science and Technology Commission of Shanghai Municipality(STCSM)under Grant No.18dz2271000
文摘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.
基金supported by the Zhejiang Natural Science Foundation of China(LQ13A010022)supported by the Qianjiang professorship of Zhejiang Province of Chinathe National Natural Science Foundation of China(11271105)
文摘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.
文摘Speed of sound data for butyl acetate＋benzene, or toluene, or o-xylene, or m-xylene, or p-xylene binary mixtures have been measured over the entire range of mole fraction at 308.15 K. The excess isentropic compressibilities （ Ks^E ） were computed from speed of sound and density data, derived from molar excess volume data. The Ks^E values were analyzed by using graph theoretical approach. The Ks^E values evaluated by graph theory compared reasonably well with their corresponding experimental values. The Ks^E data were also expressed in terms of Redlich-Kister polynomial equation to derive the coefficients and the standard deviation.
文摘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.
基金supported in part by NSFC Grant No.11371349supported in part by NSFC Grant No.11541005Shandong Provincial Natural Science Foundation(ZR2015AM001)
文摘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.
基金supported bythe National Science Foundation (USAGrant No. ATM-0758609)+1 种基金the National Aeronautics and Space Administration (USAGrant No. NNG05GR32G)
文摘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.
基金Yuxi HU was supported by the NNSFC (11701556)the Yue Qi Young Scholar ProjectChina University of Mining and Technology (Beijing)。
文摘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.
基金Supported by the NSF of Educational Department of Henan Province(200511051700)Supported by the NSF of Henan Province(200510078005)Supported by the NSF of China(10571024)
文摘The paper concerns with generalized Riemann problem for isentropic flow with dissipation, and show that if the similarity solution to Riemann problem is composed of a backward centered rarefaction wave and a forward centered rarefaction wave, then generalized Riemann problem admits a unique global solution on t≥0. This solution is composed of backward centered wave and a forward centered wave with the origin as their center and then continuous for t 〉0.
文摘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.
文摘The explicit solution to Cauchy problem for linearized system of two-dimensional isentropic flow with axisymmetrical initial data in gas dynamics is given.
文摘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%）.
基金Supported in part by the National Natural Science of China, NSF Grant No. DMS-8657319.
文摘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.
文摘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
文摘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 (<i>V<sup>E</sup></i>), deviation in viscosity (Δ<i>η</i>) and deviation in isentropic compressibility (Δ<i>K<sub>S</sub></i>) have been calculated. The results have been used to discuss the nature and strength of intermolecular interactions in these mixtures.
基金supported by the China Scholarship Council(No.202106100096).
文摘The author studies the 2D isentropic Euler equations with the ideal gas law.He exhibits a set of smooth initial data that give rise to shock formation at a single point near the planar symmetry.These solutions to the 2D isentropic Euler equations are associated with non-zero vorticity at the shock and have uniform-in-time-1/3-Holder bound.Moreover,these point shocks are of self-similar type and share the same profile,which is a solution to the 2D self-similar Burgers equation.The proof of the solutions,following the 3D construction of Buckmaster,Shkoller and Vicol(in 2023),is based on the stable 2D self-similar Burgers profile and the modulation method.
