摘要:

The waveform and velocity of second‐sound waves in superfluid helium have been studied experimentally using superconducting, thin‐film probes. The second‐sound waves were generated with electrical pulses through a resistive film. Variations in pulse power, pulse duration, and bath temperature were examined. As predicted theoretically, the formation of a shock was observed at the leading or trailing edge of the waves depending on bath temperature. Breakdown of the theoretical model was observed for large pulse powers. Accurate data for the acoustic second‐sound speed were derived from the measurements of shock‐wave velocities and are compared with previous results.

ISSN:0031-9171    

DOI:10.1063/1.862288

出版商:AIP    

年代:1978

数据来源: AIP

摘要:

The stability of the viscous flow between two parallel horizontal plates due to a constant reduced pressure gradient in a system rotating about a vertical axis is studied. The critical value of the Reynolds numberR, based on the reduced pressure gradient, is a function of a dimensionless rotation parameterT, the Taylor number. A numerical solution of the eigenvalue problem shows that (i) the minimum point for the viscous instability mode associated with plane Poiseuille flow atT=0 disappears at a value ofTof aboutT≃0.4, and (ii) forT≠0 a new instability mode appears as a result of the Coriolis effect on the basic flow and in the perturbation equations. This new instability gives the critical value ofRfor values ofTas small as 0.06.

ISSN:0031-9171    

DOI:10.1063/1.862289

出版商:AIP    

年代:1978

数据来源: AIP

摘要:

As part of a continuing study of the stability of heated laminar boundary layers in water, an experiment has been performed for the case of nonuniform surface temperature where disturbances are introduced by a vibrating ribbon and the response measured using temperature compensated hot‐film anemometry. Two types of nonuniform wall temperature distributions have been studied. These are: (a) power law distributions of the form &Dgr;T= (Tw−T∞) =Axn, and (b) step changes in wall temperature. Measured mean velocity and temperature profiles agree with solutions of the mean boundary layer equations. Measured stability characteristics for power law temperature distributions indicate that, at a fixed Reynolds number and local &Dgr;T, both the disturbance growth rate and the band of frequencies receiving amplification are reduced relative to the uniform wall temperature case whenn<0 and increase relative to the uniform wall temperature case whenn≳0. The maximum growth rate for &Dgr;T=2.78°C (5°F) andn=−0.5 is negative indicating damped disturbances at all frequencies. Disturbance growth rates for step changes in wall temperature at first decrease and then increase relative to those for uniform wall temperature as the step change location is moved downstream.

ISSN:0031-9171    

DOI:10.1063/1.862290

出版商:AIP    

年代:1978

数据来源: AIP

摘要:

The method of generalized coordinates is extended to the analysis of continuous bodies for which the degrees of freedom are independent velocity distributions in the spatial coordinates. The corresponding Lagrange equations contain generalized convective terms as well as the usual generalized forces and masses. Since the existence of a potential is not assumed, the equations of motion can be applied to media with arbitrary (possible dissipative) constitutive laws. Material deformation is characterized by the rate of strain, which is taken as the symmetric part of the velocity gradient, making the approach valid for arbitrarily large deformations. As an example, infinitesimal Rayleigh–Taylor instability is considered by analytic methods. Then, large amplitude Rayleigh–Taylor instability is represented with a single‐degree‐of‐freedom analysis that shows the development (by numerical integration) of the known spike‐and‐bubble configuration of the unstable interface. The infinitesimal stability of a plastically deforming solid and the growth of the instability to large amplitudes are also considered.

ISSN:0031-9171    

DOI:10.1063/1.862291

出版商:AIP    

年代:1978

数据来源: AIP

摘要:

A simplified formulation is presented to deal with interfacial stability problems with mass and heat transfer. For Rayleigh–Taylor stability problems of a liquid‐vapor system, it is found that the effect of mass and heat transfer tends to enhance the stability of the system when the vapor is hotter than the liquid, although the classical stability criterion is still valid. For Kelvin–Helmholtz stability problems, however, the classical stability criterion is found to be substantially modified due to the effect of mass and heat transfer.

ISSN:0031-9171    

DOI:10.1063/1.862292

出版商:AIP    

年代:1978

数据来源: AIP

摘要:

The analysis of incompressible laminar boundary‐layer flow of power‐law non‐Newtonian fluids along thin needles is presented. Similarity velocity profiles and skin friction are obtained for pseudo‐plastic, dilatant, as well as Newtonian fluids. Physical insights are gained by examining the effects of the flow behavior index and the needle size on the boundary layer flow.

ISSN:0031-9171    

DOI:10.1063/1.862293

出版商:AIP    

年代:1978

数据来源: AIP

摘要:

The concept of rapid distortion is used to simplify the Reynolds stress closure equations. A solution for axisymmetric contracting turbulent flow is obtained and compared with the results of the rapid distortion theory of Batchelor and Proudman. The fluctuation ratio u¯2¯/v2¯now predicted compares favorably with the experimental data of Uberoi. The irreversibility of rapid distortion is discussed in view of experimental evidence.

ISSN:0031-9171    

DOI:10.1063/1.862294

出版商:AIP    

年代:1978

数据来源: AIP

摘要:

Ideal magnetohydrodynamic turbulence is treated using more realistic boundary conditions than rectangular periodic boundary conditions. The dynamical equations of incompressible magnetohydrodynamics and the associated fields are expanded in a set of vector eigenfunctions of the curl. The individual eigenfunctions represent force‐free fields, but superpositions of them do not. Three integral invariants have simple quadratic expressions in the expansion coefficients: the total energy, the magnetic helicity, and the cross helicity. The invariants remain temporally constant in the face of a truncation at a large but finite number of coefficients. Boundary conditions imposed are those for a rigid, perfectly‐conducting cylindrical boundary, with an arbitrary periodicity length parallel to the axis. Canonical distributions are constructed from the invariants. Mean‐square turbulent velocity fields ⟨v2⟩ have finite values for virtually all initial conditions, including quiescient ones. The stability problem can be reformulated as a search for values of the integral invariants which will minimize ⟨v2⟩. This leads to a principle of extremal helicity, which requires a magnetic configuration which will minimize ⟨v2⟩ for a given total energy. The development of helical macroscopic structures in the cylinder as a function of increasing ratio of axial current to axial magnetic flux is predicted.

ISSN:0031-9171    

DOI:10.1063/1.862295

出版商:AIP    

年代:1978

数据来源: AIP

摘要:

It can be shown that for linearly unstable magnetohydrodynamic modes near the threshold of linear instability, the mode amplitudeA(t) evolves according to ∂2A/&Lgr;t2=&lgr;2A+&agr;A3which can lead to nonlinear stabilization, explosive instability, or eventual decay, depending on the sign of &agr;. This is demonstrated explicitly for them=1 kink modes in a sharp boundary plasma pinch.

ISSN:0031-9171    

DOI:10.1063/1.862296

出版商:AIP    

年代:1978

数据来源: AIP

摘要:

Reduction formulae for the effective, or macroscopic, Ohm’s law parameters are derived for inhomogeneous plasmas with anisotropic conductivity fluctuations having two general types of geometry: (a) elongated or shortened in the direction of the magnetic field and (b) two‐dimensional, with the direction of constant properties lying in the plane perpendicular to the magnetic field. In each case, two approaches are used: (a) a small perturbation method and (b) an approximate method where each region in the plasma is considered separately, and consistency conditions are used to relate the results corresponding to each separate region to the effective properties of the whole plasma. Both methods are found to agree well when the fluctuations are weak, but differences appear at high fluctuation levels and, for nonuniformities very elongated along B&drarr;, when the Hall parameter &bgr; is high. Comparison with available exact solutions valid at high &bgr; and strong fluctuation levels indicates that the self‐consistency method gives accurate results even in these cases. The results of these analyses are used to evaluate the performance reduction in magnetohydrodynamic channels with plasma nonuniformities of several geometries, including axial streamers, perfectly isotropic fluctuations, and fluctuations elongated along B&drarr;; the power density is reduced most strongly when &bgr; and the rms of the fluctuations are high, and also when the inhomogeneities are stretched along the magnetic field.

ISSN:0031-9171    

DOI:10.1063/1.862285

出版商:AIP    

年代:1978

数据来源: AIP