摘要:

The theory of force‐free magnetic fields is applied to equilibrium configurations of an incompressible fluid with axisymmetric motions. It is demonstrated that solutions satisfying collinear force‐free flow satisfy the vorticity equation for zero viscosity. Experimental measurements of the magnetic and flow fields of the plasmoids generated by a conical &thgr;‐pinch plasma gun are shown to be in agreement with the solutions to these equations.

ISSN:0031-9171    

DOI:10.1063/1.1711293

出版商:AIP    

年代:1964

数据来源: AIP

摘要:

Some exact solutions of the third‐order vector partial differential equation describing nonsteady flows of incompressible second‐order fluids are presented. Although periodic simple shearing flow is also discussed, the main emphasis here is on helical flows between moving coaxial cylinders, particularly periodic flows of the Couette and Poiseuille type. The calculations suggest that, for such periodic helical flows, measurements of the radial thrusts on the bounding cylindrical walls supply practicable methods for the determination of normal‐stress coefficients.

ISSN:0031-9171    

DOI:10.1063/1.1711294

出版商:AIP    

年代:1964

数据来源: AIP

摘要:

Basic fluid mechanical concepts are reformulated in order to account for some structural aspects of fluid flow. A continuous spin field is assigned to the rotation or spin of molecular subunits. The interaction of internal spin with fluid flow is described by antisymmetric stress while couple stress accounts for viscous transport of internal angular momentum. With constitutive relations appropriate to a linear, isotropic fluid we obtain generalized Navier‐Stokes equations for the velocity and spin fields. Physical arguments are advanced in support of several alternative boundary conditions for the spin field. From this mathematical apparatus we obtain formulas that explicitly exhibit the effects of molecular structure upon fluid flow. The interactions of polar fluids with electric fields are described by a body‐torque density. The special case of a rapidly rotating electric field is examined in detail and the induction of fluid flow discussed. The effect of a rotating electric field upon an ionic solution is analyzed in terms of microscopically orbiting ions. This model demonstrates how antisymmetric stress and body torque can arise in ``structureless'' fluids.

ISSN:0031-9171    

DOI:10.1063/1.1711295

出版商:AIP    

年代:1964

数据来源: AIP

摘要:

The equations of fluid mechanics are applied to the problem of small perturbations upon a finite initial strain‐rate of a viscous fluid. The magnitude of the viscosity is such that inertia forces are negligible. General solutions are developed for the time history of buckling of a fluid with an arbitrary number of layers of different viscosities under finite compressive deformation. The effect of gravity is taken into account. Numerical solutions are derived for the single layer. Results are compared with values obtained from the theory of elasticity and viscoelasticity. The interest of the theory lies in its application to problems of folding of geological structures.

ISSN:0031-9171    

DOI:10.1063/1.1711296

出版商:AIP    

年代:1964

数据来源: AIP

摘要:

The stability problem of an accelerating plane interface separating compressible fluids is formulated in general terms. In the limit of small wavelength disturbances, a generalized form of Taylor's value for the growth rate is obtained. For the particular case of constant acceleration and static isothermal equilibrium, the criterion for instability remains the same as for corresponding case of two incompressible fluids, but the growth rate is reduced for longer wavelengths.

ISSN:0031-9171    

DOI:10.1063/1.1711297

出版商:AIP    

年代:1964

数据来源: AIP

摘要:

The rotating flows of von Ka´rma´n and Bo¨dewadt are re‐examined. Complete sets of boundary data are defined for both problems in accordance with practical flow models. First‐order approximations are defined as solutions of ordinary boundary‐value problems and equivalent Volterra integral equations. The new solutions depend on three‐parameter Reynolds numbers and eliminate discrepancies of the old solutions. Numerical results are displayed for various Reynolds numbers. The critical Reynolds number below which Bo¨dewadt flows are laminar, attached, and nonoscillating is computed.

ISSN:0031-9171    

DOI:10.1063/1.1711298

出版商:AIP    

年代:1964

数据来源: AIP

摘要:

Shock waves are reflected from a wall in the presence of a transverse magnetic field. The gas is highly ionized and therefore the lines of force can be considered ``frozen in.'' In such a case the magnetic field is compressed and the Rankine‐Hugoniot relations, including magnetic pressure and magnetic energy as given by de Hoffmann and Teller, are used. The magnetic probes show an increase of the magnetic field behind the reflected shock, and the velocity of the reflected shock waves (measured from streak camera photographs) increases with increasing fields. For a constant incident velocity, the dependence of the reflected shock velocity on the magnetic field is given by a linear function:Ur2=a+bB2whereaandbare constant in a first approximation. This law has been verified by experimental results.

ISSN:0031-9171    

DOI:10.1063/1.1711299

出版商:AIP    

年代:1964

数据来源: AIP

摘要:

The Chapman‐Enskog approximation to the velocity‐energy distribution for a polyatomic gas is reinvestigated and found to yield unacceptable results for small amplitude sound waves. The solution to the linearized Boltzmann equation is then expanded in a set of orthogonal polynomials in the dynamic variables for translational and internal degrees of freedom and an iterative method of approximation is set up. This method of attack is a natural continuation of the work of Maxwell, Waldmann, of Ikenberry and Truesdell. Under some conditions the first iteration approaches the second Chapman‐Enskog approximation (or Navier‐Stokes approximation) ast→ ∞. The polynomial expansion was then truncated and the first iteration was used to calculate the heat flux, pressure tensor, and characteristic temperatures for a small amplitude sound wave. The second iteration was also investigated and was found to affect mainly only the heat fluxes. A useful formula is presented for the thermal conductivity of a polyatomic gas withNinternal degrees of freedom in the limit of zero frequency.

ISSN:0031-9171    

DOI:10.1063/1.1711300

出版商:AIP    

年代:1964

数据来源: AIP

摘要:

A method for calculating the collision integrals required for evaluating gas transport properties is described. The method is suitable for use with high‐speed computers. Results are given for the Kihara spherical core potential function and for a potential function which Guggenheim and McGlashan derived for argon. The applicability of these potential functions to argon is tested by comparison with experimental viscosity and second virial coefficient data.

ISSN:0031-9171    

DOI:10.1063/1.1711301

出版商:AIP    

年代:1964

数据来源: AIP

ISSN:0031-9171    

DOI:10.1063/1.1711302

出版商:AIP    

年代:1964

数据来源: AIP