摘要:

Recent experimental observations appear to indicate that turbulent mean flow velocity profiles with points of inflection are dynamically unstable with respect to traveling wavy disturbances. As an illustration, the description of the nonlinear development of an instability wave in the turbulent wake behind a thin body is presented on the basis of integrals of the equations of mean flow momentum, kinetic energy, and the time‐averaged disturbance kinetic energy, with the turbulent dissipation integrals relegated to phenomenological considerations. The over‐all physical mechanisms leading to the streamwise distribution of the mean flow decay and disturbance energy amplification and decay are explained through the disturbance energy production integral and the mean flow and disturbance turbulent‐dissipation integrals. The growth of the disturbance wave is limited by (1) the rapidity of turbulent mean flow decay which renders the production integral less spectacular and (2) the prominant role of the turbulent dissipation integral which draws energy away from the disturbance wave to the turbulence. These limitations and the rapidity with which events take place in the streamwise direction essentially distinguishes the instability wave in a turbulent mean flow with inflectional velocity profile from that in a corresponding laminar flow.

ISSN:0031-9171    

DOI:10.1063/1.1693325

出版商:AIP    

年代:1971

数据来源: AIP

摘要:

An incompressible two‐dimensional plane jet is analyzed using the spatial stability viewpoint. Two modes of unstable waves are found, the more unstable of which has a transverse disturbance velocity component symmetrical about the jet centerplane. Disturbance vorticity, Reynolds stress, and distributions of energetics in the cross‐stream direction are presented. Also included is a mechanism through which these jet disturbances interact with the mean flow to produce a vortex street configuration in the downstream jet field.

ISSN:0031-9171    

DOI:10.1063/1.1693326

出版商:AIP    

年代:1971

数据来源: AIP

摘要:

The linear hydrodynamic stability of a thin‐liquid layer flowing along the inside wall of a vertical tube rotating about its axis in the presence of a core‐gas flow is examined. The stability problem is formulated under the conditions that the liquid film is thin, the density and viscosity ratios of gas to liquid are small and the relative (axial) pressure gradient in the gas is of the same order as gravity. The resulting eigen‐value problem is first solved by a perturbation method appropriate to axisymmetric long‐wave disturbances. The damped nature (to within the thin‐film and other approximations made) of the nonaxisymmetric and short‐wave disturbances is noted. In view of the limitations on a truncated perturbation solution when the disturbance wavenumber is not small, an initial value method using a digital computer is presented. Stability characteristics of neutral, growing, and damped modes are presented showing the influences of rotation, surface tension, and the core‐gas flow. Energy balance in a neutral mode is also illustrated.

ISSN:0031-9171    

DOI:10.1063/1.1693327

出版商:AIP    

年代:1971

数据来源: AIP

摘要:

The stability of three‐dimensional infinitesimal waves moving in a Blasius boundary layer in a rotating flow is investigated for the situation where the rotation axis coincides with the leading edge of a semiinfinite flat plate. Primary interest is in the effect of rotation on the critical point of the neutral stability curve. The problem is formulated in terms of a sixth‐order differential equation, which reduces to the Orr‐Sommerfeld equation for zero rotation, with homogeneous boundary conditions. The eigenvalue problem thus formed is solved numerically. Results indicate a destabilizing or stabilizing effect depending on the sense of the rotation vector. This rotation effect is influenced by the spanwise wavenumber so that the effect disappears as the spanwise wavenumber vanishes. The results compare favorably with known experimental results.

ISSN:0031-9171    

DOI:10.1063/1.1693328

出版商:AIP    

年代:1971

数据来源: AIP

摘要:

It is shown that the equation relating stress and deformation in a dilute solution of polymer molecules (according to the dumbell model) may be placed in the form of the Oldroyd constitutive equation with an appropriate interpretation of constants.

ISSN:0031-9171    

DOI:10.1063/1.1693329

出版商:AIP    

年代:1971

数据来源: AIP

摘要:

Some one‐dimensional boundary value problems are considered from the viewpoint of the Wiener‐Hopf integral equation of the second kind. These include the slip flow problem and the problem of transverse oscillations in gases and use the single relaxation model equation as well as a model equation with a velocity‐dependent collision frequency. The velocity slips are related to the kernel function in a simple manner. A simple formula is obtained for the microscopic slip in the case of velocity‐dependent collision frequency. For the oscillation problem, solutions are obtained in quadrature form in a straightforward manner. This result is discussed along with the application of the present method to the problem of Knudsen flow through a long tube, the heat conduction problem, and the problem of evaporation and condensation.

ISSN:0031-9171    

DOI:10.1063/1.1693330

出版商:AIP    

年代:1971

数据来源: AIP

摘要:

An approximate method for solving the slip problems in the kinetic theory of gases is proposed, and it is shown that extremely good results can be obtained by a simple modification of Maxwell's arguments.

ISSN:0031-9171    

DOI:10.1063/1.1693331

出版商:AIP    

年代:1971

数据来源: AIP

摘要:

The pressure flow and self‐diffusion of rarefied gases through cylindrical tubes is calculated using a kinetic model, with a velocity‐independent mean free path. The model obeys the conservation laws for mass, momentum, and energy. It is shown that this “&lgr;model” gives a consistent description of both pressure flow and self‐diffusion, which is not the case for the BGK kinetic model. In addition, the slip coefficient has a value which is 8% larger than for the BGK model.

ISSN:0031-9171    

DOI:10.1063/1.1693332

出版商:AIP    

年代:1971

数据来源: AIP

摘要:

Further experimental and theoretical work on the heat loss from cylinders in flows involving low Reynolds number and binary mixtures is presented. In the experimental work techniques used previously are applied to a pair of monatomic gases, helium‐argon, so that the possible role of internal energy, as might arise when nitrogen is a participant, is clarified. The theoretical work involves an extension of the Lees‐Liu moment method to binary mixtures and application thereof to explain the observed slip effects when one gas component is of low molecular weight. It is shown that an earlier conjecture, namely, that a nonequilibrium thermodynamic behavior is involved, is correct.

ISSN:0031-9171    

DOI:10.1063/1.1693333

出版商:AIP    

年代:1971

数据来源: AIP

摘要:

A more complete solution for the near‐equilibrium, supersonic region of a spherical source flow of a monatomic gas is presented. On the basis of this solution, a method for computing meaningful reference quantities from measured data for temperature‐freezing studies is provided. The analysis brings out an explicit dependence of the Navier‐Stokes/Fourier correlations on the anisotropy, also clarifies the relationship between integration constants and reference conditions. While the degree of anisotropy generally increases with radial distance, the difference between radial and transverse stresses reaches a local maximum in the supersonic region.

ISSN:0031-9171    

DOI:10.1063/1.1693334

出版商:AIP    

年代:1971

数据来源: AIP