摘要:

The stability of ann‐layered liquid film flowing steadily down an inclined plane is investigated using linear theory. Neutral curves of all competing modes of instability have been obtained for various ratios of viscosity, density, and thickness. The interfacial mode instability due to the local downward step increase in density is found to occur only when such a density increase is large enough to provide sufficient gravitational potential. A local downward decrease in density seems to always be unstable. The interfacial mode instability associated with the local downward increase in viscosity is found to occur only if the Reynolds number is sufficiently small. The interfacial mode instability associated with the local downward step decrease in viscosity is found to be absent if the wavenumbers of the disturbances are smaller than a cutoff wavenumber.

ISSN:0031-9171    

DOI:10.1063/1.862106

出版商:AIP    

年代:1978

数据来源: AIP

摘要:

The initial value problem associated with the development of small amplitude disturbances in Rayleigh–Taylor unstable, viscous, incompressible fluids is studied. Solutions to the linearized equations of motion which satisfy general initial conditions are obtained in terms of Fourier–Laplace transforms of the hydrodynamic variables, without restriction on the density or viscosity of either fluid. When the two fluids have equal kinematic viscosities, these transforms can be inverted explicitly to express the fluid variables as integrals of Green’s functions multiplied by initial data. In addition to normal modes, a set of continuum modes, not treated explicitly in the literature, makes an important contribution to the development of the fluid motion.

ISSN:0031-9171    

DOI:10.1063/1.862107

出版商:AIP    

年代:1978

数据来源: AIP

摘要:

Numerical results on the stability of laminar flow of micropolar fluids between two parallel walls are presented. A sixth‐order stability eigenvalue problem is obtained by the usual perturbation techniques and solved by means of Noumerov difference approximations and the Newton iteration method. As far as the model considered in the present investigation is concerned, the microstructure has a destabilizing effect on two‐dimensional flows of micropolar fluids.

ISSN:0031-9171    

DOI:10.1063/1.862108

出版商:AIP    

年代:1978

数据来源: AIP

摘要:

The Burgers’ equation is considered as a simple nonlinear model equation in which to investigate energy transfer in the wavenumber domain. Spatially stationary (on the real line) random solutions are considered. The first‐order nonlinear term for large time relating the spectrum and bispectrum (Fourier transform of third‐order moments) of the random solution is determined. This nonlinear term is obtained by making use of the Hopf solution of the Burgers’ equation.

ISSN:0031-9171    

DOI:10.1063/1.862109

出版商:AIP    

年代:1978

数据来源: AIP

摘要:

An experiment was designed to measure the position of a front separating turbulent and nonturbulent fluid as the front moves away from an oscillating grid located near the planez=0. The theory predictsD∝ (Kt)1/2, whereDis the distance of the front fromz=0,t=0 is time at which the oscillation begins, andKis a quantity of the dimensions and character of eddy viscosity, called the ’’action’’ of the idealized plane energy source that replaces the grid in the theoretical model. The experimental results support the theory.

ISSN:0031-9171    

DOI:10.1063/1.862110

出版商:AIP    

年代:1978

数据来源: AIP

摘要:

When a point source explosion is initiated at the ocean surface, the shock propagated into the water is reflected at the surface as a centered expansion wave. The solution in the neighborhood of the interaction point is obtained by writing the equations of motion in the appropriate similarity variables and then changing the independent variables to polar coordinates based at the interaction point. From the zero‐order solution of the resulting equations the slopes of boundaries at the interaction point are obtained. A first‐order perturbation of this solution provides more accurate representation of the flow variables and the curvature of the shock surface near the interaction point.

ISSN:0031-9171    

DOI:10.1063/1.862111

出版商:AIP    

年代:1978

数据来源: AIP

摘要:

Surface water waves generated by surface and near surface point explosions are calculated. Taking the impulse distribution imparted at the water surface by the explosion as the overriding mechanism for transferring energy of the explosive to surface wave motion, the linearized theory of Kranzer and Keller is used to obtain the wave displacement in the far field. The impulse distribution is obtain by integrating the pressure wave over an appropriate time interval on a horizontal surface just beneath the undisturbed water surface. For surface explosions, a modified form of the similarity method first used by Collins and Holt is used to obtain the flow field. In the case of submerged explosions, the flow field is estimated by making necessary modifications to Sedov’s similarity solution to account for the venting that accompanies the interaction of the leading (blast) wave with the ocean surface. Surface waves generated by a charge at six depths of placement (h1=0.15 m, 0.30 m, 0.61 m, 0.91 m, 1.37 m, 3.05 m) are considered in addition to surface explosions. The results seem to support the existence of an upper critical depth phenomenon (of the type already established for chemical explosions) for point (nuclear) explosions.

ISSN:0031-9171    

DOI:10.1063/1.862112

出版商:AIP    

年代:1978

数据来源: AIP

摘要:

Similarity transformation and self‐similar solutions are derived for the incompressible radial flow of conducting, viscous fluids across an external, homogeneous magnetic field (parallel to the apse line) in a diffuser with electrodes in the planes &Vthgr;=±&Vthgr;0(cylindrical coordinate system). The conducting flow across the (axial) external and induced magnetic fields induces radial and azimuthal current densities. The azimuthal current density produces a net current fluxI≠0 through the electrodes which are connected by an external circuit. The eigenvalue problems for the radial velocity and induced magnetic field amplitudes are solved analytically. The external and induced magnetic fields are shown to significantly change the pressure distribution but not the onset of flow separation. This is due to the irrotational nature of the Lorentz force, ∇× (∇×B×B) =0, in which the magnetic field B(r, &Vthgr;) is axial (noncurved).

ISSN:0031-9171    

DOI:10.1063/1.862113

出版商:AIP    

年代:1978

数据来源: AIP

摘要:

The behavior of a hot, magnetized plasma brought into contact with a cold wall is studied numerically in one and two dimensions. A fully nonlinear, time‐dependent magnetohydrodynamic plasma model which includes thermal conduction, resistive diffusion, radiation, and ionization is used. The model is solved numerically with an Eulerian computer code which employs implicit finite difference methods. One‐dimensional calculations for cylindrical geometry examine the effect of the electrical properties of the wall on the plasma. Two‐dimensional calculations for cylindrical geometry show the formation of a wall‐induced instability which enhances thermal conduction losses from the plasma; the re‐emergence of short wavelengths, a new feature of unstable behavior, is evident in the calculations. Two‐dimensional calculations for toroidal geometry show that heat losses to a cold wall lead to double‐vortex convection flow of the plasma with no evidence of the formation of smaller scale convective cells.

ISSN:0031-9171    

DOI:10.1063/1.862114

出版商:AIP    

年代:1978

数据来源: AIP

摘要:

A knowledge of solid hydrogen pellet lifetimes in a plasma is critical to the design of devices to refuel tokamak fusion reactors. When the pellet is injected into the plasma, the ablated material from the pellet undergoes a transonic flow since it is heated while it expands. Calculations are done on the behavior of the transonic flow for various plasma conditions and pellet sizes. From these calculations, the ablation rate and lifetimes of the pellet are determined. A scaling law is given which allows pellet lifetimes to be easily calculated for any plasma conditions. The results of these calculations give good agreement when compared with experiments.

ISSN:0031-9171    

DOI:10.1063/1.862088

出版商:AIP    

年代:1978

数据来源: AIP