摘要:

A finite element solution of the flow between rotating spheres shows a vortex breakdown for Reynolds numbers exceeding a critical value. The result is in agreement with published results for a vortex breakdown in a cylindrical enclosure.

ISSN:0031-9171    

DOI:10.1063/1.866223

出版商:AIP    

年代:1987

数据来源: AIP

摘要:

Suppose that all the wave‐vector triad interactions that involve no wavenumber ratio that exceeds &bgr; are removed from the Navier–Stokes equation. Within a class of closures, the paradoxical effect is to enhance energy cascade through the Kolmogorov inertial range for 1<&bgr;<&bgr;c, where &bgr;cmay be as large as 8. This may have implications with regard to force‐free structures in the true Navier–Stokes dynamics.

ISSN:0031-9171    

DOI:10.1063/1.866224

出版商:AIP    

年代:1987

数据来源: AIP

摘要:

The propagation of curves with discontinuous third derivatives of the potential in a fluid described by the Hasegawa–Mima equation is studied. It is shown that the area inside a closed curve of this kind is conserved, and a law governing the evolution of the magnitude of the discontinuity is derived. The hypothesis that such curves carry soliton properties is put forward.

ISSN:0031-9171    

DOI:10.1063/1.866517

出版商:AIP    

年代:1987

数据来源: AIP

摘要:

An analytic theory is presented for the selection mechanism of a symmetric finger with a discrete set of possible width from a continuum of nonsymmetric Saffman–Taylor finger solutions of arbitrary width. Both linear and nonlinear analyses have been carried out and in almost all cases, it is shown analytically that nonsymmetric solutions do not exist for nonzero surface tension if the finger boundary is assumed to be smooth. In the other cases, numerical calculations appear to support the same conclusions. In the asymptotic range, the predicted set of countably infinite possible finger widths according to nonlinear analysis agree with the previous analytical results of Combescotetal. [Phys. Rev. Lett.56, 2036 (1986)] for a finger assumed to be symmetric about the channel centerline. The predicted coefficient of the power law dependence of finger width on surface tension for the first few of these solutions, i.e., on the branches first calculated by Mclean–Saffman [J. Fluid Mech.102, 455 (1980)], Romero (Ph.D. thesis, California Institute of Technology, 1982) and Vanden‐Broeck [Phys. Fluids26, 2033 (1983)], are in agreement with Tanveer’s [Phys. Fluids30, 651 (1987)] estimate of this coefficient based on numerical calculations of bubbles. It is also shown that the nonlinear analysis has the same qualitative features as the linear analysis and, in the asymptotic range, the agreement is close.

ISSN:0031-9171    

DOI:10.1063/1.866225

出版商:AIP    

年代:1987

数据来源: AIP

摘要:

The Biot–Savart model for a vortex filament predicts a finite time singularity in which the maximum velocity diverges as (t*−t)−1/2for the timettending tot*. The filament pairs with itself, yet remains locally smooth even though the characteristic length scales as (t*−t)1/2. A multiscale perturbative treatment of the Euler equations is developed for solutions that are locally a two‐dimensional vortex dipole centered on a slowly varying three‐dimensional space curve. For short periods of time the Euler and Biot–Savart solutions agree. Provided this correspondence persists, a sufficiently small viscosity &ngr; will not control the divergence in the maximum velocity until it is of order exp(cst/&ngr;), where cst is a constant of order the filament circulation. Singularities in the Navier–Stokes equations cannot be easily dismissed. The most questionable step in the arguments presented occurs for &ngr;=0, namely whether the Euler vortex dipole solutions break down when they self‐stretch.

ISSN:0031-9171    

DOI:10.1063/1.866226

出版商:AIP    

年代:1987

数据来源: AIP

摘要:

The linear stability of Couette flow composed of two layers of immiscible fluids, one lying on top of the other, is considered for the special case when the two fluids have similar mechanical properties. The interfacial eigenvalue is found in closed form by considering the two‐fluid problem as a perturbation of the one‐fluid problem. The importance of the role played by the viscosity difference, when one of the fluids is in a thin layer, is illustrated.

ISSN:0031-9171    

DOI:10.1063/1.866227

出版商:AIP    

年代:1987

数据来源: AIP

摘要:

The linear stability of plane three‐layer vertical Poiseuille flow is considered. The layers are composed of two immiscible fluids, one next to the walls and one centrally located. The fluids have different viscosities and densities and surface tension effects are included. Intuitively, an analogy with the concentric Hagen–Poiseuille flow is expected and the similarities and differences are investigated. The ability of heuristic reasoning to predict which arrangements are more likely to be observed is tested. Numerical results concerning low Reynolds numbers, as well as the behavior of eigenvalues close to the first criticality of the one‐fluid problem, are presented.

ISSN:0031-9171    

DOI:10.1063/1.866228

出版商:AIP    

年代:1987

数据来源: AIP

摘要:

Shown here are the dispersion relation, the oscillation frequency, and the critical Marangoni number for the onset of oscillatory interfacial instability in a horizontal single‐ or two‐component liquid layer heated from above or below when the upper deformable surface is open to the ambient air. It is shown that for vanishingly small gravity the temperature gradient for the onset of instability also becomes negligibly small thus indicating the major importance and the potential danger of Marangoni–Be´nard instability in experiments under microgravity conditions.

ISSN:0031-9171    

DOI:10.1063/1.866229

出版商:AIP    

年代:1987

数据来源: AIP

摘要:

The effect of the buoyancy‐driven convection on the separation of the two constituents of a binary mixture in a long cylindrical cell is considered. This cell is designed to measure the thermal diffusion (Soret) coefficient of that mixture in a spatial (microgravity) environment. Such a cell, heated from the ends, is subjected to a nearly constant axial temperature gradient that generally presents some inclination with respect to the gravity vector, giving rise to low but three‐dimensional motions. In space applications this inclination (with respect to residual gravity) is generally not knownapriori. A three‐dimensional simulation based on a false transient scheme with finite difference techniques is carried out in order to study the influence of the cell inclination on low convective motions. Two small values of a Grashof number, relevant for space applications (Gr=1 and Gr=3), and three values of the Soret parameter (S=−0.5,S=0, andS=0.5) have been considered. Characteristics of the flow and of its influence on the separation of constituents are given for several inclinations. Particularly interesting results are discussed for the vertical situations. Attention is focused on a molten (AgI–KI) mixture with a Prandtl number of 0.6 and a Schmidt number of 60, contained in a cylinder with an aspect ratio of 6.

ISSN:0031-9171    

DOI:10.1063/1.866230

出版商:AIP    

年代:1987

数据来源: AIP

摘要:

Using numerical simulations of the anelastic partial differential equations, convective flow in a two‐dimensional polytropic atmosphere is investigated. Fixing the aspect ratio at unity and choosing the viscosity as the order parameter, the numerical solutions have indicated a variety of dynamic behavior including (i) oscillatory motion with a period of order the eddy turnover time, (ii) quasiperiodic motion with a long period much longer than an eddy turnover time, and (iii) at least two branches of solutions in certain regimes.

ISSN:0031-9171    

DOI:10.1063/1.866231

出版商:AIP    

年代:1987

数据来源: AIP