摘要:

A method of investigating the interaction of free‐surface waves with viscous wakes is described. The method consists in constructing a viscous‐wake solution to the Oseen equations that satisfies the three linearized free‐surface conditions appropriate to a viscous fluid. The solution is characterized by a singularity which simulates approximately the effect of a body. More general flows of the same type can be formed by superposition. The solution obtained is believed to be the first one to represent explicitly a viscous wake in the presence of a free surface.

ISSN:0031-9171    

DOI:10.1063/1.1691899

出版商:AIP    

年代:1968

数据来源: AIP

摘要:

The Lagrangian‐history direct‐interaction approximation for Burgers' equation yields ak−2inertialrange spectrum and an infinite‐Reynolds‐number similarity solution which describes stationary, decaying sawtooth shock waves. This solution differs by a numerical factor from an exact statistical solution of Burgers' equation into which almost all spatially periodic, zero‐mean, infinite‐Reynolds‐number initial ensembles are expected to evolve. The different inertial‐range predictions of the approximation for Burgers' equation and Navier‐Stokes dynamics (wherek−5/3results) are directly associated with the effects of pressure‐induced accelerations on Lagrangian correlation times.

ISSN:0031-9171    

DOI:10.1063/1.1691900

出版商:AIP    

年代:1968

数据来源: AIP

摘要:

The production of high‐speed shocks in shock tubes has been limited to levels below1.3cm/&mgr;secby excessive radiation from the initially stagnant arc‐heated driver gas. This limitation can be removed by adding the required energy to a flowing driver gas in a device in which the static temperature is maintained at a sufficiently low level as to keep the radiation losses small. The magnetic annular arc has demonstrated such capabilities in applications for space propulsion and solar wind simulation. Based on this past experience, a magnetic annular arc driver was constructed for a38.1‐mm(1.5in.)shock tube and was operated at an average power level of 200 MW for50 &mgr;secat a voltage of 1kV. Helium was used as the driver gas and shock speeds in excess of2cm/&mgr;secwith a test time of approximately5 &mgr;secwere obtained in air. It was also determined that the empirical scaling relations for the magnetic annular arc operating voltage and anode heat transfer observed in earlier applications are still applicable at the higher‐power densities and mass flows appropriate to this experiment.

ISSN:0031-9171    

DOI:10.1063/1.1691901

出版商:AIP    

年代:1968

数据来源: AIP

摘要:

The structure of normal ionizing shock waves is studied. Following a discussion of some of the work done in this field, the shock equations are integrated for a simple model. The main assumptions are that the effects of viscosity and thermal conductivity are confined to a very narrow region (thermal shock) across which there is no change in ionization, and that the post‐shock gas is only slightly ionized. As an example, the equations governing the structure of a shock in argon have been integrated. The results of these calculations justify the use of the assumptions made in deriving the equations.

ISSN:0031-9171    

DOI:10.1063/1.1691902

出版商:AIP    

年代:1968

数据来源: AIP

摘要:

The flow past a solid body is analyzed by means of the Boltzmann equation. It is shown that for small Mach numbers a formal linearization is affected by the same difficulties as the Stokes linearization in continuum fluid mechanics. In particular, it is proved that the linearized Boltzmann equation does not provide bounded solutions for the flow past an axisymmetric body. As a consequence, an inner‐outer expansion must be constructed, and the linearization is to be reinterpreted as the first step of the inner expansion; the outer one being very similar to the Hilbert and Chapman‐Enskog expansions.

ISSN:0031-9171    

DOI:10.1063/1.1691903

出版商:AIP    

年代:1968

数据来源: AIP

摘要:

An approach for evaluating the thirteen moments of the Boltzmann collision integral for electronion and electron‐neutral collisions in an ionized gas is developed. It is an approximation based on the smallness of the electron mass and is different from the approach of Enskog, Chapman and Cowling, Grad, Burgers and others. The initial inspiration is conceived after a study of the works of Lorentz, Druyvesteyn, Davydov, Allis and others. With the new approach, it is easy to include even higher‐order moments and to treat distribution functions which are not locally Maxwellian even in the zeroth order, as well as to study problems with large diffusion velocities and enhanced electron temperatures. The approach is valid, however, only for electron‐ion and electron‐neutral collisions. For these collisions, the thirteen‐moments results agree with those of Burgers when the distribution functions are locally Maxwellian in the zeroth order and the electron temperatures is not enhanced. Application of the new approach to various problems is demonstrated.

ISSN:0031-9171    

DOI:10.1063/1.1691904

出版商:AIP    

年代:1968

数据来源: AIP

摘要:

A kinetic equation for a homogeneous and uniformly rotating stellar system is established, based on statistical theory. The theory includes both the effects of direct gravitational encounters and collective processes. The expressions for the dynamic friction and diffusion tensor are provided. Based on these results, characteristic relaxation times may be discussed readily.

ISSN:0031-9171    

DOI:10.1063/1.1691905

出版商:AIP    

年代:1968

数据来源: AIP

摘要:

An exact equation of evolution, with the structure of the diffusion equation, is derived for the phase‐space probability density of a system whose Hamiltonian is random. No assumption need be made about the magnitude of the fluctuations nor about their time scale. In the limit of short correlation time and weak correlations, the equation reduces to the equation of Birmingham, Northrop, and Fa¨lthammar. The reduction of the Fokker‐Planck equation to diffusion form is also demonstrated.

ISSN:0031-9171    

DOI:10.1063/1.1691906

出版商:AIP    

年代:1968

数据来源: AIP

摘要:

The equilibrium correlation functions have been calculated for a high‐temperature plasma with enough accuracy to yield the thermodynamic functions to second order in terms of the plasma parameter. First, the classical solutions have been obtained for a two‐component plasma and a many‐component plasma and compared with the results for an electron gas in a uniform positive background. Second, the convergent solutions have been obtained starting with the quantum Bogoliubov‐Born‐Green‐Kirkwood‐Yvon (BBGKY) hierarchy. In the calculation, exchange effects as well as the Heisenberg effect have been taken into account. Also some corrections of the quantum BBGKY hierarchy concerning the symmetry properties have been given.

ISSN:0031-9171    

DOI:10.1063/1.1691907

出版商:AIP    

年代:1968

数据来源: AIP

摘要:

On the basis of the unified theory, it is proved that the four kinetic equations obtained by Kihara, Baldwin, Frieman and Book, and by Perkins are equivalent to each other and exact in the sense that the Coulomb logarithms with exact numerical factors in the arguments can be obtained by use of any one of them.

ISSN:0031-9171    

DOI:10.1063/1.1691908

出版商:AIP    

年代:1968

数据来源: AIP