摘要:

The stability of an exact solution of the Navier‐Stokes equations for the flow between two parallel horizontal plates due to a constant reduced pressure gradient in a system rotating about a vertical axis is studied. For zero rotation the stability problem reduces to the classical Orr‐Sommerfeld equation for the stability of plane Poiseuille flow. The variation of the critical Reynolds number with rotation is determined by an expansion procedure for small values of the dimensionless rotation parameter (Taylor number). The effect of small rotation is destabilizing. By using known results for the stability of the Ekman boundary layer an asymptotic result for the critical Reynolds number is obtained for large values of the Taylor number.

ISSN:0031-9171    

DOI:10.1063/1.1694263

出版商:AIP    

年代:1973

数据来源: AIP

摘要:

The instability of a circular cylindrical jet of liquid in air is studied on the assumption that the wavenumberkof the disturbance is complex while its frequency&sgr;is real. This implies that the disturbance grows with distance along the jet, but that it does not grow with time. The occurence of such disturbances is called spatial instability, in contrast to the temporal instability studied by Rayleigh and others, in whichkis real and&sgr;is complex. It is found that there are infinitely many unstable modes for the axially symmetric case and also for each of the asymmetric cases. In the case of high velocity jets, one of these modes for the symmetric case corresponds to the mode Rayleigh found. However, it is not the most rapidly growing mode. Both analytical and numerical solutions of the dispersion equation are given forkas a function of&sgr;and of the dimensionless jet velocity.

ISSN:0031-9171    

DOI:10.1063/1.1694264

出版商:AIP    

年代:1973

数据来源: AIP

摘要:

The occurrence of thermal oscillations in a wedge‐shaped Be´nard cell containing water‐methanol mixtures is described and evidence is presented to suggest that the oscillations arise from an instability in the roll‐cell convection produced by the wedge shape. Steady oscillations observed recently in a Benard cell containing water‐ethanol mixtures have been attributed to the Soret effect and this suggestion is critically discussed.

ISSN:0031-9171    

DOI:10.1063/1.1694265

出版商:AIP    

年代:1973

数据来源: AIP

摘要:

A theoretical model is proposed to describe the entrainment of ambient air by a rising thermal. The model is appropriate for the first few revolutions of a strongly heated thermal whose motion is dominated by its initial conditions. At sufficiently early times, only the outer edge of the thermal is turbulent. The ambient gas mixes with the thermal gas along the turbulent interface and is convected into the thermal along streamlines. The gas densities and species concentrations on each streamline are obtained by superimposing a turbulent mixing layer on the edge of Hill's spherical vortex. Solutions are obtained in terms of the dimensionless ratio of the mixing length to the thermal radius(l/a )and the entrainment coefficient is shown to be directly proportional tol/a.

ISSN:0031-9171    

DOI:10.1063/1.1694266

出版商:AIP    

年代:1973

数据来源: AIP

摘要:

A universal velocity defect law for turbulent boundary layers developing in adverse pressure gradients is proposed. The velocity scale for this law is independent of the wall shear but related instead to the local maximum in the Reynolds stress profile. The proposal and its implications are checked against a very large body of experimental results and a partial connection between the mean velocity field and the shear stress field is established. A comparison between the present theory and the mixing length theory is presented. The experimental data do not appear to support many of the assumptions nor the predictions of the mixing length theory. The distinction between equilibrium and nonequilibrium layers made by Clauser is shown to be unnecessary as all classes of layers appear to conform to the new universal velocity defect law proposed, provided that the maximum shear stress is sufficiently larger than the wall shear stress.

ISSN:0031-9171    

DOI:10.1063/1.1694267

出版商:AIP    

年代:1973

数据来源: AIP

摘要:

The temperature and concentration fields produced by turbulent mixing of two reactants undergoing a one‐step, very rapid, irreversible, exothermic reaction are studied. Temperature and concentration fields decay in two stages: kinetically driven and diffusion controlled. Stochastic solutions are derived for the first stage, the asymptotic state of which displays all the characteristics of species segregration. In particlar, only a weak correlation between the concentration and temperature fields is generated in the first stage. For the special case of equal mass diffusivities and a Lewis number of one the solution to the second stage is obtained in terms of the solution of a nonreacting binary mixing problem. An approximate solution for Lewis numbers different from one is proposed. The temperature field seems to decay with an effective thermal diffusivity determined by the smaller of the molecular mass and thermal diffusivities.

ISSN:0031-9171    

DOI:10.1063/1.1694268

出版商:AIP    

年代:1973

数据来源: AIP

摘要:

In turbulent flow situations the histograms constructed in the individual realization mode of laser anemometry are biased. The biasing occurs because a larger than average volume of fluid, and hence a larger than average number of scattering centers, pass through the probe volume during periods when the velocity is faster than the mean. Similarly, a smaller volume of fluid and a smaller number of scattering particles pass through the probe volume during periods when the velocity is slower than the mean. The proper weighting function needed to correct the biased data is the inverse of the instantaneous velocity vector. However, an analysis using turbulent flow models show that corrections based only upon the streamwise component of the velocity vector are adequate for many flow situations.

ISSN:0031-9171    

DOI:10.1063/1.1694269

出版商:AIP    

年代:1973

数据来源: AIP

摘要:

A nonlinear second‐order analysis shows that all small disturbances of the interface between a semi‐infinite, inviscid liquid and a uniform supersonic gas stream are unstable, as according to linear theory. Moreover, the growth rates increase with the amplitude of the disturbance.

ISSN:0031-9171    

DOI:10.1063/1.1694270

出版商:AIP    

年代:1973

数据来源: AIP

摘要:

TheK‐dependent diffusion constant of 0.3&mgr; Teflon particles in the critical mixture isooctane‐nitroethane has been measured for0.001 < T − T c < 2 °C. The results are presented along with a simple theory that gives good agreement by considering the surface energy force on the particle due to concentration fluctuations.

ISSN:0031-9171    

DOI:10.1063/1.1694271

出版商:AIP    

年代:1973

数据来源: AIP

摘要:

A simple method of construction of linearized kinetic models is proposed which is based upon the equivalence of moments of theNth‐order modeled collision operator and the moments of the full collision operator calculated with theNth‐order approximation to the distribution function. This method is used to construct a third‐order model of the linearized cross‐collision operator for a general multicomponent monatomic gaseous mixture, not restricted to Maxwell molecules. In addition, this method is used to extend the Hanson‐Morse diatomic gas model of the Wang Chang‐Uhlenbeck collision operator to a polyatomic gas. Also presented is a new method of formally extending the Gross‐Jackson modeling procedure to multicomponent monatomic mixtures. It is shown that the method of constructing mixture models based on the equivalence of moments is identical to this new procedure. In addition, the Gross‐Jackson modeling procedure recently developed for mixtures by Boley and Yip is analyzed. It is shown that, under a certain weak restriction, their method is equivalent to the simpler Gross‐Jackson procedure — and leads to the same expression for theNth‐order model, except for the manner of specification of the constant in the diagonal approximation.

ISSN:0031-9171    

DOI:10.1063/1.1694272

出版商:AIP    

年代:1973

数据来源: AIP