摘要:

The functional integral representing the grand canonical partition function of the Kac, Uhlenbeck, and Hemmer model is approximated, in a systematic way, to give a much simpler integral representing one‐dimensional Brownian motion with absorption. It is shown that the paths which make the dominant contributions to this integral are those which correspond to alternating regions of high and low density in the fluid. An interpretation of these paths as representing configurations of droplets and bubbles is given. The pressure of the system is obtained by summing over the droplet‐bubble configurations, and it is shown that there is no phase transition for any finite value of the range of the attractive potential. A number of properties of the droplets are determined. The relation of this work to inverse range expansions and other recent works is discussed.

ISSN:0031-9171    

DOI:10.1063/1.1693562

出版商:AIP    

年代:1971

数据来源: AIP

摘要:

A derivation of hydrodynamic equations from the linearized Boltzmann equation is presented which is based upon Zwanzig's projection operator method. This is obtained in the simple compact form of linearized Burnett equations with frequency and wavelength dependent transport coefficients, for which explicit expressions are given for well‐behaved intermolecular potentials. The effects of the initial distribution function may be included, although for long times the initial state terms disappear. This disappearance of the initial state terms implies that for long times the general hydrodynamic equations and the Chapman‐Enskog hydrodynamic equations agree. The latter are exact for all times for a special initial state. As an application of the theory, an expression is found for the dispersion equation for sound propagating in a gas, that holds for any well‐behaved intermolecular potential.

ISSN:0031-9171    

DOI:10.1063/1.1693563

出版商:AIP    

年代:1971

数据来源: AIP

摘要:

The kinematic motion of(N+1)geostrophic (Bessel) vortices is studied. Initially, the vortices are positioned near a uniformly rotating equilibrium configuration which consists ofNvortices of equal strength&ggr;equally spaced on a circle of radiusa, and one vortex of strength&ggr;0at the center of the circle. One length scale&kgr;−1is associated with each of the vortices, the limiting case&kgr; = 0being the classical logarithmic vortex. The linearized stability of this equilibrium configuration is studied over the range of the three parameters:N≥2, 0≤ (&kgr;a) < ∞, and− ∞ <(&ggr;0/&kgr;) < ∞. Over the entire range of the parameters, there are double‐zero eigenvalues, which imply that the motion of the center vortex is inherently nonlinear. Numerical computations show that nonlinear effects are important in a parametric transition region embracing both the stable and unstable sides of the neutral stability curves for the circle vortices, even for small initial perturbations. The stability of the center vortex is not well represented by the neutral stability curves. In addition, the nonlinear motion away from an unstable equilibrium toward a stable equilibrium configuration is studied numerically.

ISSN:0031-9171    

DOI:10.1063/1.1693564

出版商:AIP    

年代:1971

数据来源: AIP

摘要:

The limits of using retarded motion expansions of simple fluid theory are examined. The possible existence of two types of instability for parallel flows of second‐order fluids is shown. For one of these instabilities the second‐order fluid assumptions are not valid and mathematical stability results do not bear any relation to real fluid behavior in this region. Apparent contradictions in previous papers are resolved.

ISSN:0031-9171    

DOI:10.1063/1.1693565

出版商:AIP    

年代:1971

数据来源: AIP

摘要:

A linear stability analysis of a horizontal layer of the reactive fluid mixture(A2A)which is undergoing the surface catalyzed nonisothermal reaction (A2&lrhar2;2A) is performed. It has been found that including the heat of reaction in our analysis leads not only to a modification of the convective instability observed for the isothermal reactive fluid, but also to a whole new class of instabilities for fluids with negative (gravitationally stable) steady‐state density gradients. This new class of instabilities resulting from the heat of reaction is referred to as “thermochemical” instabilities. The mathematically similar thermosaline evaporation problem, describing the evaporation of water from the surface of a salt solution, is also examined and found to exhibit similar stability characteristics.

ISSN:0031-9171    

DOI:10.1063/1.1693566

出版商:AIP    

年代:1971

数据来源: AIP

摘要:

The Navier‐Stokes equations are solved numerically for the flow of elastico‐viscous fluid near a rotating disk by expanding the velocity components in powers of a small parameterK0*. The main effect of elasticity is to increase the magnitude of the velocity components and to decrease the magnitude of the turning moment on the disk.

ISSN:0031-9171    

DOI:10.1063/1.1693567

出版商:AIP    

年代:1971

数据来源: AIP

摘要:

A differential equation is derived relating the density&rgr;−and the density gradient&rgr;x−behind a shock wave when the region ahead of the wave has always been at equilibrium. The existence of a critical density gradient&lgr;(generally negative) is established: For a compression shock&rgr;−will increase, decrease, or remain constant according as&rgr;x−is less than, greater than, or equal to&lgr;.&lgr;is shown to be related to the critical amplitude for acceleration waves; an experimental procedure for determining&lgr;as a function of&rgr;−is given.

ISSN:0031-9171    

DOI:10.1063/1.1693568

出版商:AIP    

年代:1971

数据来源: AIP

摘要:

A characteristic equation describing the stability of an electrified fluid cylinder is derived taking into account effects due to the electric field, surface tension, viscosity, and inertia. The electric field causes the cylinder to be unstable subsequent to nonaxisymmetric deformations of the interface. For relatively inviscid fluids electrification can make the growth rates for nonaxisymmetric disturbances almost as large as the rates for axisymmetric forms. It is found that viscous effects tend to damp axisymmetric motions more than motions accompanying a sinuous deformation; thus, the sinuous mode may be the most unstable form of disturbance in many situations. The combined effects of viscosity and the electric field act so that the cylinder manifests the greatest instability at wavelengths about as large as the circumference of the cylinder, when viscous effects are paramount, in contrast to Rayleigh's result for an unelectrified fluid cylinder.

ISSN:0031-9171    

DOI:10.1063/1.1693569

出版商:AIP    

年代:1971

数据来源: AIP

摘要:

Two independent methods (spark tracer and magnetohydrodynamic) are described for the measurement of the velocity of the gas in the free stream of a high enthalpy shock tunnel. Comparison is made with calculated results.

ISSN:0031-9171    

DOI:10.1063/1.1693570

出版商:AIP    

年代:1971

数据来源: AIP

摘要:

Unsteady, one‐dimensional magnetohydrodynamic shock formation in a shock tube has been studied by numerical solution of the single‐fluid continuum equations, using numerical dissipation as the only diffusion mechanism. The results are qualitative inasmuch as the exact shapes of the various profiles are not predicted. However, considerable physical insight has been gained, particularly concerning the early‐time evolution of the shock wave and its separation from the drive‐current layer. By appropriate scaling, these results can be compared with experiments, and are useful in their interpretation. Many of the departures of experimental results from ideal theory can be explained in terms of finite dissipation, without introducing anomalous effects.

ISSN:0031-9171    

DOI:10.1063/1.1693571

出版商:AIP    

年代:1971

数据来源: AIP