摘要:

In the classical inviscid theory of a vortex ring, the velocity at a point near the vortex ring becomes singular due to terms ofr−1and lnrwhereris the shortest distance from the point to the vortex ring. Also the velocity of the vortex ring depends on the logarithm of the effective radius of the cross section of the vortex ring and is infinite for zero radius. The effect of the viscosity in the inner core of the vortex ring is now included and the inner viscous solution is matched with the classical inviscid solution of the outer region by the boundary layer technique. By means of the systematic matching, the singularities ofr−1and lnrin the classical inviscid theory is removed. By the requirement that the velocity at the center of the viscous core is finite, a unique and finite value is obtained for the velocity of the translation of the vortex ring which is decreasing with respect to time as − ln (&ngr;&tgr;), where &ngr; is the kinematic viscosity. From this analysis, the effective radius of the cross section of the vortex ring can be identified as 2(&ngr;&tgr;)½. The variable &tgr; is transformed from the time variabletby the relationship &tgr; = ∫0tR(t′)dt′/R(t), whereR(t) is the radius of the ring.

ISSN:0031-9171    

DOI:10.1063/1.1762240

出版商:AIP    

年代:1967

数据来源: AIP

摘要:

The hydrodynamic stability of a plane, two‐dimensional, incompressible wall jet subjected to small disturbances was examined by a linearized theory. The critical Reynolds numberR&dgr;cwas determined to be about 57. The eigenvalues and eigenfunctions were numerically calculated for neutral stability (ci= 0) as well as for several cases of amplification of the wave (ci> 0).

ISSN:0031-9171    

DOI:10.1063/1.1762241

出版商:AIP    

年代:1967

数据来源: AIP

摘要:

The boundary layer is observed in low‐speed flow over a dispersively‐coupled system of acoustic resonators. It is found that oscillations in the laminar layer are strongly excited by this model of a passive, flexible wall. The ``geometry'' of this process differs from that expected with a real membrane, however, due to the details of the wall construction. A different set of laminar oscillations dominates the flow over the middle of the surface, producing turbulence in a manner controlled by the spanwise variations in the wall. The importance of the nature of this transition process to other shearing flows is discussed.

ISSN:0031-9171    

DOI:10.1063/1.1762242

出版商:AIP    

年代:1967

数据来源: AIP

摘要:

The results of numerical calculations for two‐dimensional Be´nard convection between rigid boundaries are reported and compared with recent numerical and experimental values reported by other investigators. Values of the Nusselt number, Nu, in the range of Rayleigh number,R, from 2000 to 20 000 are presented. The degree of resolution of a grid point representation necessary to give an accuracy of Nu of 1% is determined. The implications of this requirement show that some previous numerical investigations must have involved fairly large errors in the heat flux and possibly even spurious time oscillations. It is also shown that recent experimental determinations of Nu agree quite well with calculations when the fluid has a large Prandtl number, &sgr;. However, for water (&sgr;=6.8) the discrepancy between numerical calculations and experimental measurements is quite large (14% atR= 20 000).

ISSN:0031-9171    

DOI:10.1063/1.1762243

出版商:AIP    

年代:1967

数据来源: AIP

摘要:

For thermal convection between horizontal plates a certain Rayleigh number greater than the critical value must be attained before well‐defined, unsteady temperature fluctuations occur. Their appearance is found to be a strong function of Prandtl number, and has apparently been explained for large Prandtl number by a theory of Howard. These fluctuations at a given point midway between plates are intermittent in appearance over a considerable range in Rayleigh number. The Rayleigh number at which the intermittency essentially ceases and irregular fluctuations are nearly always present is determined and also found to be strongly dependent upon Prandtl number. There is no apparent association between the development of these short‐period fluctuations and the heat‐flux transitions of Malkus.

ISSN:0031-9171    

DOI:10.1063/1.1762244

出版商:AIP    

年代:1967

数据来源: AIP

摘要:

The low Reynolds number flow past a heated infinite cylinder is studied for cases involving significant variation of fluid properties, and when thermal and velocity slip is present at the wall. Initially, the inner and outer asymptotic expansions for the flow field variables are derived for an arbitrary thermal conductivity‐temperature relationship. The corresponding Nusselt number, developed in terms of the expansion parameter &egr; = [ln (4/RePr) − &ggr;¯ + &bgr;]−1(where Re is the Reynolds number, Pr is the Prandtl number, &ggr;¯ is the Euler's constant and &bgr; is the thermal slip parameter), is valid to order &egr;3. For the special case &lgr; =T&ohgr;an explicit relationship Nu = Nu (Re, Pr, &tgr;, &ohgr;, &bgr;) is given, where &tgr; = (T′w−T′∞)/T′∞. It is shown that the continuum and slip Oseen‐type analyses of Cole and Roshko, and Levey, respectively, are zeroth‐order approximations for the Nusselt number in the limit &tgr; → 0. The zeroth‐order drag coefficient is also given in the formCDo=CDo(Re, &tgr;, &ohgr;,f), wherefis the velocity slip parameter.

ISSN:0031-9171    

DOI:10.1063/1.1762245

出版商:AIP    

年代:1967

数据来源: AIP

摘要:

The heat loss from wires in nitrogen, helium, and mixtures thereof has been measured at low Reynolds numbers and has been compared with the theory of Kassoy. The data in nitrogen agree well with previous data and with the theory for continuum flow and validate the experimental techniques. The helium data exhibit large slip effects at low Knudsen numbers due to the low thermal accommodation coefficient of helium; good agreement with the theory of Kassoy for slip effects is found. Some data exhibiting slip in helium‐nitrogen mixtures are given. A mixture rule for the effective thermal accommodation coefficient in binary mixtures is suggested.

ISSN:0031-9171    

DOI:10.1063/1.1762246

出版商:AIP    

年代:1967

数据来源: AIP

摘要:

The compressible flow of a viscous, heat‐conducting gas around a corner is considered; in particular, the viscous corrections in the expansion region are calculated. The solutions are written in terms of asymptotic expansions, valid in the region far, compared to a viscous length, from the corner, so that the zeroth‐order solutions are the classical Prandtl‐Meyer solutions. The method of inner and outer expansions is used where the inner region encloses the first Mach line emanating from the corner. It is shown that the first effect of the transport properties in the expansion region is to generate terms either of order Re−1(inverse Reynolds number) or of order Re−1log Re, depending on the dependent variable considered.

ISSN:0031-9171    

DOI:10.1063/1.1762247

出版商:AIP    

年代:1967

数据来源: AIP

摘要:

Probability density measurements of the turbulent velocities were made at several positions in a curved mixing layer. The probability densities reveal the intermittent nature of the flow, which is fully turbulent in the center of the mixing layer but nonturbulent far away from the mixing layer. By using an ``intermittency analyzer'' in combination with a pulse height analyser, the statistical properties of the ``fully turbulent'' flow were obtained. An important result of this study is that the ``apparent'' transfer of energy, which appeared to be up the energy gradient, is actually due to a difference in mean velocity between the fully turbulent and nonturbulent fluid. The nonturbulent fluid contained within the convex bulges of turbulent fluid fluctuates wildly in velocity, but is almost free of vorticity.

ISSN:0031-9171    

DOI:10.1063/1.1762248

出版商:AIP    

年代:1967

数据来源: AIP

摘要:

A hierarchy of coupled equations for multipoint turbulent velocity distribution functions is derived. These equations resemble the Bogoliubov‐Born‐Green‐Kirkwood‐Yvon equations of kinetic gas theory. The properties of the distribution functions and the equations are discussed and compared with kinetic theory.

ISSN:0031-9171    

DOI:10.1063/1.1762249

出版商:AIP    

年代:1967

数据来源: AIP