摘要:

Constitutive equations describing small perturbations on viscometric flows are derived. The relations are similar in form to the linear integral stress‐deformation relations of infinitesimal viscoelasticity theory. Restrictions imposed by material symmetry and by incompressibility are discussed. It is shown that certain relations between the stress‐relaxation moduli and the basic viscometric functions must be satisfied for self‐consistency of the theory.

ISSN:0031-9171    

DOI:10.1063/1.1762197

出版商:AIP    

年代:1967

数据来源: AIP

摘要:

The stability of a layer of elastico‐viscous liquid (Oldroyd's liquid B) flowing down an inclined plane under the action of gravity is investigated. An eigenvalue problem governing the stability of the flow against wave formation is formulated and solved for small values of wave number. It is found that the presence of elasticity in the liquid lowers the value of the critical Reynolds number.

ISSN:0031-9171    

DOI:10.1063/1.1762198

出版商:AIP    

年代:1967

数据来源: AIP

摘要:

An approximate method for finding the critical conditions for stability with respect to penetrative cellular perturbation is proposed. The method is tested by finding the critical conditions for stability of flow between counter‐rotating cylinders and by comparing them with those obtained by more rigorous methods and by experiments. The same method is later applied for Be´nard convection arising in a horizontal layer of fluid with constant unstable density gradient and penetrating into a layer of fluid with constant stable density gradient situated above the unstable layer. It is found that the classical rigid‐free boundary solution corresponds to the limiting case of infinite stability on top of the unstable layer. For small stability on top the solutions have some of the features of Chandra's columnar perturbations and the build up of cumulus towers in the tropics. The critical value of the Rayleigh number in this case is found to be much smaller than that obtained by not taking penetration into account.

ISSN:0031-9171    

DOI:10.1063/1.1762199

出版商:AIP    

年代:1967

数据来源: AIP

摘要:

Spherically averaged spectral densities of quantities appearing in the turbulent energy equation are assumed to be locally similar: i.e., to depend on external parameters in a similar way when referred to local scales of flux and length. Dynamical equations are given for the influence of production (including anisotropy), viscosity, buoyancy, magnetic field, and elasticity. General solutions of these equations are obtained implicitly, and the leading term in a series expansion explicitly. This similarity is shown to be a generalization of the ideas of Kolmogorov, of the modified Onsager cascade used by Corrsin, and of the formulation of Kovasznay and Shur for the influence of viscosity and buoyancy. In the case of viscosity, the prediction of a spectral cutoff by the Kovasznay formulation is seen to be misleading, and due to the retention of only the leading term in the expansion.

ISSN:0031-9171    

DOI:10.1063/1.1762200

出版商:AIP    

年代:1967

数据来源: AIP

摘要:

The evolution of a weak, random initial magnetic field in a highly conducting, isotropically turbulent fluid is discussed with the aid of the exact expression for initial growth of the magnetic energy spectrum. Equipartition arguments, the vorticity analogy, and the known turbulence approximations all are found inadequate for predicting whether the magnetic energy eventually dies away or grows exponentially. This is true for any ratio of magnetic diffusivity &lgr; to kinematic viscosity &ngr;. The possibilities of eventual growth and eventual decay are therefore both admitted, and, for each, the shape of the magnetic‐energy spectrum in the case &lgr; » &ngr; is estimated by simple dynamical arguments. If there is growth, it is concluded that the magnetic spectrum below the Ohmic cut‐off eventually reaches equipartition with the kinetic‐energy spectrum roughly in the fashion predicted by Biermann and Schlu¨ter, with the principal exceptions that the spectrum of kinetic energy in the equipartition inertial range evolves to the formk−3/2and that equipartition is maintained, with rapidly falling spectrum, through part of the Ohmic dissipation range. The evolution of the magnetic spectrum in the weak‐field &lgr; » &ngr; regime is also computed numerically with a simplified transfer approximation suggested by the Lagrangian‐history direct‐interaction equations. This calculation turns out to yield an eventual very weak exponential growth of magnetic energy.

ISSN:0031-9171    

DOI:10.1063/1.1762201

出版商:AIP    

年代:1967

数据来源: AIP

摘要:

The problem of a nonconducting sphere moving slowly through a current‐carrying, incompressible, viscous fluid is re‐examined by taking fluid inertia into consideration. Stokes and Oseen expansions appropriate for flow near and far from the sphere are constructed and matched properly. The result shows that a standing eddy first appears behind the sphere at a Reynolds number Re = 24(3+4Rh)−1,Rhbeing the magnetic pressure number. The effect of current is to hasten flow separation and to enlarge the reverse‐flow region. The drag of the sphere is found to be 1 + Re (3 +Rh)/8 times the Stokes value.

ISSN:0031-9171    

DOI:10.1063/1.1762202

出版商:AIP    

年代:1967

数据来源: AIP

摘要:

The characteristics of light emission from hydrodynamic cavitation are given. Changes were examined for small variations in water temperature, pressure, and gas content. Using oxygen, nitrogen, and xenon dissolved in water, the shapes, intensities, and pulse height spectra for individual light pulses were determined. With this information, combined with time integrated spectrophotometric data, the validity of some current theories is considered.

ISSN:0031-9171    

DOI:10.1063/1.1762203

出版商:AIP    

年代:1967

数据来源: AIP

摘要:

The characteristic equations for a two‐dimensional, steady, supersonic gas flow with source terms and chemical reactions are developed. A continuum mixture of gas and particles with negligible volume is used to define the particle source terms. Mass sources which give rise to chemical reaction with the surrounding gas are considered. The mass, momentum and heat sources are defined to be compatible with experimental data for a single particle.

ISSN:0031-9171    

DOI:10.1063/1.1762205

出版商:AIP    

年代:1967

数据来源: AIP

摘要:

Small angle x‐ray scattering data have been obtained for concentrated suspensions of southern bean mosaic virus containing approximately 20, 10, and 5 gm virus per 100 ml of suspension. In addition, the scattering from independent virus particles was determined from the scattering curves for dilute suspensions. The Zernike‐Prins equation was used to compute the pair correlation functions for the concentrated suspensions. The pair correlation functions indicated relatively weak interparticle forces. The effective distance of closest approach of two particles was appreciably greater than the particle diameter, which was approximatley 285 Å. The interaction potential energy for a pair of molecules was estimated by three different approximate theories.

ISSN:0031-9171    

DOI:10.1063/1.1762206

出版商:AIP    

年代:1967

数据来源: AIP

摘要:

The symmetry property of a bimodal shock wave is shown to be destroyed by using the Bhatnagar‐Gross‐Krook equation. By using a modified BGK model, the symmetry property is recovered.

ISSN:0031-9171    

DOI:10.1063/1.1762207

出版商:AIP    

年代:1967

数据来源: AIP