摘要:

Nonlinear periodic waves in a stratified fluid stationary with respect to a rotating cylindrical system are studied. The case to be considered is that of an incompressible, inviscid fluid with free surface rotating about a rigid circular cylinder and pulled toward the axis of the cylinder by a constant body force. Critical angular speeds, near which such periodic waves are possible, are determined by the eigenvalues of an eigenvalue problem, and the equation governing the wave profiles is then obtained by a compatibility condition. With slight modification, the method developed is applied to other cases of interest.

ISSN:0031-9171    

DOI:10.1063/1.1692300

出版商:AIP    

年代:1969

数据来源: AIP

摘要:

A theoretical analysis was carried out to determine the stability properties of unsteady natural convection. In this analysis a perturbation technique was used in conjunction with a special type unsteady base flow for transient natural convection between two infinite parallel vertical plates. Perturbation analysis yields a sequence of ordinary differential equations to describe the coupled time‐dependent disturbance behavior. The equations were solved for a number of values of Grashof and wavenumbers and for a wide range of rate of acceleration and deceleration to determine the unsteady base flow stability characteristics. A growth factor was used to determine the stability properties, and it was found that an accelerating (decelerating) base flow is more (less) stable than a steady base flow when compared at common values of the instantaneous Grashof number. This tendency was found to increase rapidly at first and then to slowly decrease with increasing rate of change of the base flow.

ISSN:0031-9171    

DOI:10.1063/1.1692301

出版商:AIP    

年代:1969

数据来源: AIP

摘要:

Steady flows of a thin layer of viscous liquid on a horizontal plane induced by the nonuniformity of surface tension at its free surface are treated. If the film is very thin, surface‐tension effects dominate gravity effects. Under that circumstance and away from vertical boundaries, a binomial of depthhof the liquid layer is a harmonic function of the Cartesian coordinatesxandyin a horizontal plane, and the surface tension is a function ofh. Near any vertical boundary there is a velocity boundary layer whose thickness is of the order ofh. The velocity distribution in this boundary layer is given explicitly. The diffusion of the surface material affecting the surface tension is considered. Steady flows of a liquid film induced by gravity are also discussed. Simple solutions are possible if the film flows over a horizontal plane.

ISSN:0031-9171    

DOI:10.1063/1.1692302

出版商:AIP    

年代:1969

数据来源: AIP

摘要:

In turbulent shear flows, it is generally known from the mechanical energy equation that a production term of turbulent energy, normally implying a transfer of energy from the mean motion to the turbulence, contributes through a significant physical process to the permanence or quasisteady state of turbulence in the presence of convective, diffusive, and dissipative influences. It is shown that certain flows with asymmetric mean velocity distribution may displaylocalized areasin which the production term is a loss in the energy balance and consequently of the same sign as the dissipation. For better terminology the phenomenon of negative production is here calledenergy reversal. The existence of zones of energy reversal also implies a concept ofzones of opposing shear. In this localized region, the Reynolds stress and the viscous shear stress oppose each other unlike what is expected in normal boundary layer and pipe flows. A modified relationship, relating the Reynolds stress to the mean viscous stress, taking into account small‐ and large‐scale effects, proposed by Hinze and Be´guier is justified on the basis of experimental evidence.

ISSN:0031-9171    

DOI:10.1063/1.1692303

出版商:AIP    

年代:1969

数据来源: AIP

摘要:

An independence hypothesis is proposed which predicts the evolution of the amplitude of Fourier modes of the concentration fluctuation field for a substance undergoing a second‐order single‐species isothermal reaction in homogeneous turbulence. The hypothesis is that the time history of such an amplitude is a product of its time history due to reaction and its time history due to turbulent mixing and diffusion. A sufficient condition for the hypothesis to be applicable is that the spectral decay due to reaction alone exhibits wavenumber similarity with a constant length scale. When the initial fluctuation intensity is high enough, the initial decay of the mean concentration (mean‐square concentration) as predicted by the hypothesis gives a lower (upper) bound on the actual initial rate of decay. It is also demonstrated by numerical calculation of a particular initial isotropic concentration spectrum in the absence of turbulence that the independence hypothesis and the predictions of a valid closure for this problem differ by no more than an order of magnitude over the entire time history of decay for all possible values of the diffusivity and reaction rate. When turbulence is present, the long time evolution of the mean concentration and the mean‐square concentrations as predicted by the hypothesis are in excellent agreement with previous computations employing direct interaction.

ISSN:0031-9171    

DOI:10.1063/1.1692304

出版商:AIP    

年代:1969

数据来源: AIP

摘要:

An artificial random force is introduced into Burgers' model equation for turbulence. This forced model equation is solved numerically as an initial‐value problem. Both the driving force and initial velocity field are assumed Gaussian and are generated by a white noise process. Many statistical properties of this model for turbulence are studied. By adjusting the external force, the turbulence can reach an equilibrium state. The velocity correlation function and energy spectrum are calculated for the equilibrium turbulence. It is found that the energy spectrum falls off as the inverse second power of the wavenumber. The velocity correlation function is similar to the result obtained in real turbulence experiments. With Gaussian random driving force and Gaussian initial velocity field, it is found that the velocity field remains very nearly Gaussian by comparing the fourth‐order velocity correlation with the quasinormal assumption. Although the process remains very nearly Gaussian, it is found that the projection of the process on the initial white noise process becomes smaller and smaller. This is to be expected, since the dynamic system is escaping from the original random base.

ISSN:0031-9171    

DOI:10.1063/1.1692305

出版商:AIP    

年代:1969

数据来源: AIP

摘要:

The problem of the steady axially symmetric expansion of a monatomic gas from an orifice into a vacuum is considered. The reservoir conditions are such that the local Knudsen number is initially small. It is noted that the near continuum solution, valid near the orifice, is not uniformly valid far downstream where the local mean free path may be comparable with some characteristic length. A valid solution of Boltzmann's equation, for Maxwell molecules, is deduced for this far field core region. Near the gas‐vacuum front, predicted by the equilibrium solution, this expansion procedure also breaks down. It is shown that a further scaling of the variables in Boltzmann's equation, consistent with this limit, can be found and the corresponding moment equations deduced. However, in contrast to the behavior in the core, these equations no longer form a closed set.

ISSN:0031-9171    

DOI:10.1063/1.1692306

出版商:AIP    

年代:1969

数据来源: AIP

摘要:

The fluxes of a mixture of gases diffusing through a porous medium in the normal diffusion region are derived, with emphasis on the flux ratio at uniform pressure. The Boltzmann equation is solved by the moment method, putting boundary conditions in the solution. Maxwell's method is shown to be inadequate, and it is found that, besides the well‐known mass effect, a molecular interaction effect appears in the expression of the flux ratio. Thus, the experimental deviations from the usual law are explained. Then, the flux ratio is experimentally determined for an isobaricN2‐C2H4mixture and found to be in qualitative agreement with theory. Finally the experimental results on the motion of spheres in nonhomogeneous gaseous mixtures are explained for the first time.

ISSN:0031-9171    

DOI:10.1063/1.1692307

出版商:AIP    

年代:1969

数据来源: AIP

摘要:

Molecular velocity distribution functions have been measured throughout a normal,M = 1.59helium shock wave that was formed in a low‐density wind tunnel. The measurements were obtained by using the electron beam fluorescence technique. Throughout the shock transition, distributions of random velocities were observed from directions both parallel and perpendicular to the flow. Also, direct measurements were made of the density and the flow velocity. The shock wave satisfied the continuity, momentum, and energy equations within the accuracy of the measurements. Parallel and perpendicular temperatures compare favorably to predictions derived from the Navier‐Stokes equations. In the upstream portion of the shock the distributions of parallel peculiar molecular velocities predicted according to the Chapman‐Enskog first iterate differ significantly from the experimental results, although as mentioned the second moments or temperatures agree with the Navier‐Stokes values.

ISSN:0031-9171    

DOI:10.1063/1.1692308

出版商:AIP    

年代:1969

数据来源: AIP

摘要:

The transient energy transfer during expansion of a plane layer of radiating gas bounded by a strong shock is investigated. The inviscid, nonconducting gas is assumed to be perfect and in local thermodynamic equilibrium. A shock fitting procedure is used which completely specifies the motion and position of the shock by an iterative solution of the partial differential equations and the Rankine‐Hugoniot shock boundary conditions. For a gray gas, results are presented for parameters of physical interest. Results obtained for transparent, gray, and nongray models are compared.

ISSN:0031-9171    

DOI:10.1063/1.1692309

出版商:AIP    

年代:1969

数据来源: AIP