摘要:

A method of generating a class of exact solutions for three‐dimensional boundary layer flows is presented. These are solutions to the initial value problem for steady, incompressible flow. In one type the history upstream of the initial plane is known; in a second type this history is not known. A power law pressure gradient exists in the streamwise direction but the cross flow decays under zero cross pressure gradient. The essential restriction for obtaining exact solutions is that all quantities not depend on the cross stream coordinate. The solutions are obtained as expansions in terms of eigenfunctions. The cross flow and the streamwise vorticity decay algebraically with powers that depend on the pressure gradient and eigenvalues. An S‐shaped initial profile has a decay rate approximately twice as great as a C‐shaped initial profile; the former requires a few hundred boundary thicknesses to decay appreciably. The decay rate is only mildly dependent on the streamwise pressure gradient. These results of physical interest in three‐dimensional boundary layer flows are obtained without extensive numerical calculations.

ISSN:0031-9171    

DOI:10.1063/1.1694489

出版商:AIP    

年代:1973

数据来源: AIP

摘要:

A numerical scheme of integration is devised to integrate the unsteady laminar boundary‐layer equations with partly reversed flows. The neighborhood of the vanishing skin friction which has been considered up to now as the location of separation, is found to be nonsingular while a typical Goldstein‐type of a traveling singularity is discovered farther downstream. This singularity is interpreted according to the theory of Sears and Telionis as unsteady boundary‐layer separation. The features of the flow in the neighborhood of the singularity are investigated.

ISSN:0031-9171    

DOI:10.1063/1.1694490

出版商:AIP    

年代:1973

数据来源: AIP

摘要:

Uniform potential flow past two equal spheres in contact, parallel to the common tangent plane, is analyzed. The velocity is found to diverge approaching the point of contact asr −2+√2. Application of this result to critical velocity phenomena in superfluid helium is discussed.

ISSN:0031-9171    

DOI:10.1063/1.1694491

出版商:AIP    

年代:1973

数据来源: AIP

摘要:

A solution for the dynamical behavior of the energy spectrum for a homogeneous isotropic fluid is obtained from the equations for the turbulent multipoint distribution functions. The calculated spectrum shows reasonable agreement with experimental data.

ISSN:0031-9171    

DOI:10.1063/1.1694492

出版商:AIP    

年代:1973

数据来源: AIP

摘要:

The simplified statistical theory developed earlier is extended to the wall shear flows. This is accomplished by formulating the contribution of the smaller eddies to the observable properties, which becomes significant very close to the wall, from an available stochastic analysis of the Navier‐Stokes equation. Turbulent Couette flow is then analyzed by the use of the theory. Comparison of the Couette flow solutions obtained with the available experimental results shows that the present theory satisfactorily describes the rather detailed turbulence structure of the flow field as well as the mean velocity profile and the surface shear.

ISSN:0031-9171    

DOI:10.1063/1.1694493

出版商:AIP    

年代:1973

数据来源: AIP

摘要:

The possibility of acoustic amplification in a gas subjected to an external means of overpopulating internal energy levels has been explored theoretically. The basic concept that the temperature variation of the sound wave controls the flow of energy from the source to translation must take into account the internal structure of the gas. When the gas is pumped optically, the strong temperature dependence of the collisional de‐excitation rate constants is included in addition to the temperature and pressure dependence of the optical absorption coefficient considered by others. The resulting attenuation or amplification of sound has been calculated both for a two‐level and a multilevel gas. For illustrative purpose, a 90% CO‐10% H2numerical example has been developed. This example demonstrates that sound amplification should be experimentally observable.

ISSN:0031-9171    

DOI:10.1063/1.1694494

出版商:AIP    

年代:1973

数据来源: AIP

摘要:

The results of numerical integrations of three‐dimensional equations of motion of ions subject to given electric and magnetic fields are presented. The fields represent those which may exist in the pinch phase of the plasma focus, although here they depend only on the radial coordinate. The ions initially have Maxwellian velocity distributions, and their trajectories are interpreted in terms of single‐particle constants of the motion. Two models of the axial electric fieldEzare considered. For strongEzaway from the axis, there is a cyclotron acceleration which leads to ion heating. For positiveEzon the axis, ions within a Larmor radius of the axis undergo very efficient acceleration; the results for this new model are in general agreement with experimental results.

ISSN:0031-9171    

DOI:10.1063/1.1694495

出版商:AIP    

年代:1973

数据来源: AIP

摘要:

A theory appropriate to the description of the stable astronElayer in experiments up to the present time is developed. When field cancellation is small and it can be assumed that theElayer is perturbed by collisions with a uniform background neutral gas, it is shown the axial and radial distributions are described by simple cylindrical diffusion equaitons. The model predicts loss rates of theElayer as well as self‐consistent radial and axial density profiles.

ISSN:0031-9171    

DOI:10.1063/1.1694462

出版商:AIP    

年代:1973

数据来源: AIP

摘要:

The spatial and temporal distribution of the energy deposited by a fast deuteron in a hot deuterium plasma is calculated taking into account energy loss to thermal ions by scattering that results from elastic nuclear processes in addition to the usual Coulomb interaction with thermal electrons and ions. The method of calculation and the approximations involved are discussed, and numerical results are given for a deuterium plasma at normal liquid density. For plasma electron temperatures above approximately 10 keV, the effect of including nuclear processes ind‐dscattering is to cause the energy of a fast deuteron to be deposited nearer to its point of origin in space and time with relatively more energy going directly to ions.

ISSN:0031-9171    

DOI:10.1063/1.1694463

出版商:AIP    

年代:1973

数据来源: AIP

摘要:

Electrostatic modes are shown to be excited, in two‐dimensional plasma equilibrium configurations, with frequency and parity characteristics such as to significantly affect the orbits of trapped ions by proper mode‐particle resonances in regimes where the single‐particle collision mean free paths are considerably longer than the periodic particle excursions. In particular, new modes driven by the ion temperature gradient are shown to become unstable in the presence of trapped particles under less restrictive conditions and with considerably larger transverse wavelengths than the ion temperature gradient driven modes arising in a one‐dimensional equilibrium configuration. The resulting enhancement in the transport of ion thermal energy across the magnetic field is discussed.

ISSN:0031-9171    

DOI:10.1063/1.1694464

出版商:AIP    

年代:1973

数据来源: AIP