摘要:

Rarefactive ion‐acoustic solitons have been observed in a two‐electron‐temperature plasma. Some of the characteristics can be interpreted by the solution of the Kortweg–de Vries (K–dV) equation. The Mach number of the solitons is a function of the temperature ratio of hot and cold components.

ISSN:0031-9171    

DOI:10.1063/1.865717

出版商:AIP    

年代:1986

数据来源: AIP

摘要:

The effect of side wall heat transfer on the stability of natural convection in a vertically oriented finite slab of saturated porous material is considered. All six bounding faces are impermeable. A temperature contrast between the top and bottom horizontal surfaces provides the mechanism for destabilization. The narrow vertical end walls are perfectly insulated. The thermal conditions on the broad vertical side walls range from perfectly insulating to fully conducting as determined by the value ofB, the Biot number based on slab height. An asymptotic analysis of the general solution is made in the narrow gap limit &egr;≪1, where &egr; is the cross‐slab width‐to‐height ratio. In this case the relevant heat transfer variable isB¯=&egr;B, the Biot number based on the narrow slab width. In the limit &egr; → 0 whenB¯=O(1), including the caseB¯→∞ that corresponds to a linear side wall temperature profile, tall, vertical, three‐dimensional, finger‐like cells are found at the critical Rayleigh numberRc=&pgr;2/&egr;2. In the limitB¯ → 0 corresponding to perfect insulation, one obtains two‐dimensional,O(1) aspect ratio rolls with axes normal to the side walls at the critical valueRc=4&pgr;2. These two‐dimensional rolls predominate only forB¯=O(&egr;2), and transition to tall narrow three‐dimensional cells occurs whenO(&egr;2)≪ B ≪ O(1).

ISSN:0031-9171    

DOI:10.1063/1.865718

出版商:AIP    

年代:1986

数据来源: AIP

摘要:

A linear stability analysis of the Be´nard problem for two layers of different fluids lying on top of each other and bounded by free surfaces is considered. The fluids are assumed to be similar and perturbation methods are used to calculate the interfacial eigenvalue in closed form. The case of the Rayleigh number and wavenumber of the disturbance being close to the first criticality of the one‐fluid Be´nard problem has been investigated in a previous paper [Phys. Fluids28, 2699 (1985)], and was found to exhibit both overstability and convective instability. In this paper, the Rayleigh number is assumed to be less than that of the first criticality of the one‐fluid problem, and in this situation, overstability does not occur. An unexpected result is that by an appropriate choice of parameters, it is possible to find linearly stable arrangements with the more dense fluid on top.

ISSN:0031-9171    

DOI:10.1063/1.865719

出版商:AIP    

年代:1986

数据来源: AIP

摘要:

The three‐dimensional linear instability of parallel shear flows is investigated through simple geometrical constructions based on the classical Squire transformation. It is shown that if a profile is unstable for a finite Reynolds number and some value of (total) horizontal wavenumber, this profile is also unstable for all larger Reynolds numbers and the same wavenumber. In particular, the direction of the unstable mode tends toward the perpendicular as the Reynolds number increases, thus providing the viscous/shear balance required for resistive instability. The example of plane Poiseuille flow is discussed in detail, and the results compared with classical viscous and inviscid stability criteria.

ISSN:0031-9171    

DOI:10.1063/1.865720

出版商:AIP    

年代:1986

数据来源: AIP

摘要:

Three sufficient conditions for stability are established for a general class of rotating flows with the velocity and the density distribution varying in both the axial and radial directions. Two are the classical Richardson criteria in the axial and radial directions. The third, measured by a newly defined Richardson number, acts as a constraint on the other two. The newly defined Richardson number is a ratio between the interaction of the density variations with the force fields and the interaction of the velocity gradients in two directions. The former interaction is a result of the pressure restraint condition and is measured by a new Brunt–Va¨isa¨la¨ frequency. The latter interaction determines whether the velocity gradients in the second direction strengthen or weaken the resultant shear effect. Because of the generality of the flow profiles being considered, the criteria established in this investigation are valid for a wide range of problems in oceanographic and atmospheric studies.

ISSN:0031-9171    

DOI:10.1063/1.866011

出版商:AIP    

年代:1986

数据来源: AIP

摘要:

Progressive gravity waves at the interface between two unbounded fluids are considered. The flow in each fluid is taken to be potential flow. The problem is converted into a set of integrodifferential equations, reduced to a set of algebraic equations by discretization, and solved by Newton’s method together with parameter variation. Meiron and Saffman’s [J. Fluid Mech.129, 213 (1983)] calculations showing the existence of overhanging waves are confirmed. However, the present calculations do not support Saffman and Yuen’s [J. Fluid Mech.123, 459 (1982)] conjecture that the waves are geometrically limited (i.e., that solutions exist until the interface intersects itself). It is proposed that along a solution branch starting with sinusoidal waves of small amplitude, one reaches solutions with vertical streamlines and then overhanging waves. Continuing on this branch, one returns to nonoverhanging waves and then back toward a wave with vertical streamlines. It is suggested that this succession of patterns and accompanying oscillation in wave characteristics is repeated indefinitely. Graphs of the results are included.

ISSN:0031-9171    

DOI:10.1063/1.865721

出版商:AIP    

年代:1986

数据来源: AIP

摘要:

The solution for the perturbation growth of a shock wave striking a density discontinuity at a material interface is developed. The Laplace transformation of the perturbation results in an equation which has a simple solution for weak shock waves. The solution for strong shock waves may be given by a power series. It is assumed that the equation of state is that of an ideal gas. The four independent parameters of the solution are the ratio of specific heat for each material, the density ratio at the interface, and the incoming shock strength. Properties of the solution which are investigated include the asymptotic behavior at large times of the perturbation velocity at the interface, the vorticity near the interface, and the rate of decay of the solution at large distances from the interface. The last is much weaker than the exponential decay in an incompressible fluid. The asymptotic solution near the interface, in addition to a constant term, consists of a number of slowly decaying discrete frequencies. The number is roughly proportional to the logarithm of the density ratio at the surface for strong shocks, and decreases with shock strength. For weak shocks the solution is compared with results for an incompressible fluid. Only interface perturbation velocities which tend to zero at large times lead to a limited deformation of the interface. It is found that these are possible only for density ratios less than about 1.5.

ISSN:0031-9171    

DOI:10.1063/1.865722

出版商:AIP    

年代:1986

数据来源: AIP

摘要:

A Langevin model appropriate to constant property turbulent flows is developed from the general equation for the fluid particle velocity increment proposed by Pope in an earlier paper [Phys. Fluids26, 404 (1983)]. This model can be viewed as an analogy between the turbulent velocity of a fluid particle and the velocity of a particle undergoing Brownian motion. It is consistent with Kolmogorov’s inertial range scaling, satisfies realizability, and is consistent with second‐order closure models. The objective of the present work is to determine the form of a second‐order tensor appearing in the general model equation as a function of local mean quantities. While the model is not restricted to homogeneous turbulence, the second‐order tensor is evaluated by considering the evolution of the Reynolds stresses in homogeneous flows. A functional form for the tensor is chosen that is linear in the normalized anisotropy tensor and in the mean velocity gradients. The resulting coefficients are evaluated by matching the modeled Reynolds stress evolution to experimental data in homogeneous flows. Constraints are applied to ensure consistency with rapid distortion theory and to satisfy a consistency condition in the limit of two‐dimensional turbulence. A set of coefficients is presented for which the model yields good agreement with available data in homogeneous flows.

ISSN:0031-9171    

DOI:10.1063/1.865723

出版商:AIP    

年代:1986

数据来源: AIP

摘要:

The results of direct numerical simulations of chemically reacting, turbulent mixing layers are presented. The reaction considered is a binary, irreversible reaction with no heat release, so that only the effect of the turbulence on the chemical reaction is investigated. The simulation results are shown to be consistent with similarity theory, and are found to be in approximate agreement with laboratory data, even though there are no adjustable parameters in the method.

ISSN:0031-9171    

DOI:10.1063/1.865724

出版商:AIP    

年代:1986

数据来源: AIP

摘要:

TheFNmethod is used, in the field of rarefied gas dynamics, to develop a complete solution for the cylindrical Poiseuille flow and thermal creep problems. The linearized Bhatnagar–Gross–Krook (BGK) model and purely diffuse reflection at the surface are used to describe the physical problem. The derived set of singular integral equations is solved by polynomial expansion and collocation. By choosing suitableFNapproximations, the solution of both problems under consideration is accomplished with a single matrix inversion, minimizing computational time and effort. The converged numerical results for the flow rates and the velocity profiles are correct to four significant figures, thus supporting the results of previous authors achieved by other methods.

ISSN:0031-9171    

DOI:10.1063/1.865725

出版商:AIP    

年代:1986

数据来源: AIP