摘要:

A boundary‐layer argument shows that, paradoxically, a variable tangential stress which is greatest at the wave crests and least in the wave troughs produces a thickening of the boundary layer on therearslopes of the waves and a thinning on the forward slopes. In deep water, a variable tangential stress⊥is precisely equivalent to a normal stressi⊥in quadrature with the tangential stress. The corresponding rate of growth of the waves is calculated.

ISSN:0031-9171    

DOI:10.1063/1.1692549

出版商:AIP    

年代:1969

数据来源: AIP

摘要:

An integral equation is derived for the propagation of small amplitude surface waves perpendicular to a movable strip lying in the free surface. The transmission and reflection amplitudes are calculated with a variational approximation valid for long and medium wavelengths. Typical numerical results are presented.

ISSN:0031-9171    

DOI:10.1063/1.1692550

出版商:AIP    

年代:1969

数据来源: AIP

摘要:

A singular perturbation analysis of acoustic‐gravity waves is presented in which not only the dependent but also the independent variables are expanded in power series of a small parameter&egr;. The series expansion of the independent variables enables us to correct, at each stage of the expansion, the forward characteristic lines of the governing equations and in turn, to determine the crossing of adjacent characteristics, if such crossings indeed occur for the chosen initial conditions. For waves propagating upwards in the verticalzdirection and satisfying the condition that atz = 0, u = u0sin&ohgr;t, it is shown that a shock develops in the flow. The distance at which the shock takes place is given for different values of the index of refraction and the wave form obtained is compared to the usual linear solution.

ISSN:0031-9171    

DOI:10.1063/1.1692551

出版商:AIP    

年代:1969

数据来源: AIP

摘要:

The problem of the growth or decay of second‐order (acceleration) discontinuities using the theory of singular surfaces is investigated for the particular case of a medium consisting of a perfect gas exhibiting density and temperature fields which vary exponentially. Relations are derived for the amplitude of such waves as well as for the critical times for those cases where the acceleration discontinuities increase without bound, the criterion used for the development of a velocity or shock discontinuity.

ISSN:0031-9171    

DOI:10.1063/1.1692552

出版商:AIP    

年代:1969

数据来源: AIP

摘要:

Experiments in an electric shock tube operating at a few Torr have shown compression waves moving ahead of the luminous discharge plasma for Mach numbers below 12 to 15. Failure to observe this separation at higher velocities is attributed to mixing caused by a Taylor unstable density distribution and the deceleration of the flow. The unstable distribution is caused by the density rise accompanying ionization behind the shock front. A model based on these assumptions, which correctly predicts separation conditions in argon, is presented. The structure of the shock waves (pressure, flow velocity, and temperature) is approximately described by blast wave theory. The deviations are primarily due to real gas effects.

ISSN:0031-9171    

DOI:10.1063/1.1692553

出版商:AIP    

年代:1969

数据来源: AIP

摘要:

An investigation and extension of similarity concepts has been undertaken for describing shock‐initiated flux compression devices. The similarity equations are developed for finite variable conductivities. Compatibility of an induced homology for the preshock magnetic field is seen to give rise to a flux compression constraint. This constraint relates the shock speed to the growth rate of the field and the homology characterizing preshock density gradients. Use of a nonstatic piston in similarity problems is questioned on physical grounds. Numerical examples are calculated for field compression with an infinite postshock magnetic Reynolds number in order to obtain sample postshock field profiles. Analytic solutions can be obtained when the dimensionless Alfve´n velocityB2/R ≳ 1. Some flux slipping appears to be required to obtain nonsingular solutions.

ISSN:0031-9171    

DOI:10.1063/1.1692554

出版商:AIP    

年代:1969

数据来源: AIP

摘要:

An exact solution is found for the motion of a conducting solid of revolution rotating in an infinite conducting viscous fluid at rest at infinity. The magnetic field is the sum of a uniform field directed parallel to the axis and an induced toroidal field. Explicit expressions for the fluid velocity, magnetic field, and couple on the solid are given for the case of a sphere.

ISSN:0031-9171    

DOI:10.1063/1.1692555

出版商:AIP    

年代:1969

数据来源: AIP

摘要:

The small‐amplitude motions of a plane interface between two fluids stressed by an initially perpendicular electric field are investigated. The fluids are modeled as Ohmic conductors and the convection of the surface charge caused by the dynamic interplay of interfacial electric shear stresses and the viscous stresses is highlighted. The influence of viscosity on instability growth rates in the zero‐shear stress limits of perfectly conducting and perfectly insulating interfaces is described and compared to cases involving electrical shear stresses. Detailed attention is given to the instability of an interface between fluids having electrical relaxation times long compared to times of interest. It is shown that, for many common liquids, even a slight amount of surface charge makes the interface unstable at a considerably lower voltage than would be expected from theories based on the dielectrophoretic limit of no interfacial free charge. Experiments, performed using high‐frequency ac stresses, gradually increased dc fields, and abruptly applied dc fields, support the theoretical model. In the general case, the electric Hartmann number is identified as an index to the dominance of the electric shear stresses over the viscous shear stresses in determining the interfacial convection of free charge.

ISSN:0031-9171    

DOI:10.1063/1.1692556

出版商:AIP    

年代:1969

数据来源: AIP

摘要:

The pair distribution function for a classical one‐component plasma is obtained by summing terms of the Montroll‐Mayer cluster expansion ofg(r)as modified by Meeron and Hirt for the Coulomb potential. A simple class of diagrams in this nodal expansion gives the asymptotic form ofg(r)for long distance as a modified Debye form. We obtain results exact toO(&Lgr;2 log &Lgr;)where&Lgr; = 1/4&pgr;n&lgr;D3is the plasma parameter. The analysis shows that for&Lgr;larger than a critical value&Lgr;cthe long‐distance form ofg(r)changes from the Debye form to a damped oscillatory form in qualitative agreement with the Monte Carlo calculations of Brush, Sahlin, and Teller. Numerical calculations done on the simplest form of our result agree moderately well with the Monte Carlo results over the entire range ofrfor&lgr; ≤ 2, and represent a substantial improvement over the nonlinear Debye‐Hu¨ckel result.

ISSN:0031-9171    

DOI:10.1063/1.1692557

出版商:AIP    

年代:1969

数据来源: AIP

摘要:

The elastic collision operator for a relativistic Lorentz gas is converted to differential form. The Fokker‐Planck “limit” is deduced. The Fokker‐Planck form is obtained for a relativistic electronion gas. Possible implications for a relativistic plasma are discussed.

ISSN:0031-9171    

DOI:10.1063/1.1692558

出版商:AIP    

年代:1969

数据来源: AIP