ISSN:1070-6631    

DOI:10.1063/1.3480124

出版商:AIP    

年代:1994

数据来源: AIP

摘要:

The characteristics and bicharacteristics of the linearized equations of motion for compressible fluid are identical to the wave fronts and rays, respectively, calculated by Fermat’s least‐time principle of geometric acoustics. The bicharacteristics emanating from the middle of a compressible shear layer curve so as to hinder communication in the axial direction.

ISSN:1070-6631    

DOI:10.1063/1.868426

出版商:AIP    

年代:1994

数据来源: AIP

摘要:

Numerical evidence is presented that two‐dimensional motion of a large region of incompressible, inviscid fluid due to the motion of a point vortex in a rectangular container leaves does not stir certain finite regions. Such regions are formed by means of the Poincare´ mapping in the regular domain for a nonintegrable Hamiltonian system of fluid particle motion.

ISSN:1070-6631    

DOI:10.1063/1.868047

出版商:AIP    

年代:1994

数据来源: AIP

摘要:

A two‐dimensional model for quasigeostrophic flow which exhibits an analogy with the three‐dimensional incompressible Euler equations is considered. Numerical experiments show that this model develops sharp fronts without the need to explicitly incorporate any ageostrophic effect. Furthermore, these fronts appear to become singular in finite time. The numerical evidence for singular behavior survives the tests of rigorous mathematical criteria.

ISSN:1070-6631    

DOI:10.1063/1.868050

出版商:AIP    

年代:1994

数据来源: AIP

摘要:

The steady motion of an advancing meniscus in a gas‐filled capillary tube involves a delicate balance of capillary, viscous, and intermolecular forces. The limit of small capillary numbers Ca (dimensionless speeds) is analyzed here with a matched asymptotic analysis that links the outer capillary region to the precursor film in front of the meniscus through a lubricating film. The meniscus shape in the outer region is constructed and the apparent dynamic contact angle &THgr; that the meniscus forms with the solid surface is derived as a function of the capillary number, the capillary radius, and the Hamaker’s constant for intermolecular forces, under conditions of weak gas–solid interaction, which lead to fast spreading of the precursor film and weak intermolecular forces relative to viscous forces within the lubricating film. The dependence on intermolecular forces is very weak and the contact angle expression has a tight upper bound tan &THgr;=7.48 Ca1/3for thick films, which is independent of the Hamaker constant. This upper bound is in very good agreement with existing experimental data for wetting fluids in any capillary and for partially wetting fluids in a prewetted capillary. Significant correction to the Ca1/3dependence occurs only at very low Ca, where the intermolecular forces become more important and tan &THgr; diverges slightly from the above asymptotic behavior toward lower values.

ISSN:1070-6631    

DOI:10.1063/1.868076

出版商:AIP    

年代:1994

数据来源: AIP

摘要:

This work concerns the spreading of viscous droplets on a smooth rigid horizontal surface, under the condition of complete wetting (spreading parameterS≳0) with the Laplace pressure as the dominant force. Owing to the self‐similar character foreseeable for this flow, a self‐similar solution is built up by numerical integration from the center of symmetry to the front position to be determined, defined as the point where the free‐surface slope becomes zero. Mass and energy conservation are invoked as the only further conditions to determine the flow. The resulting fluid thickness at the front is a small but finite (≊10−7) fraction of the height at the center. By comparison with experimental results the regime is determined in which the spreading can be described by this solution with good accuracy. Moreover, even within this regime, small but systematic deviations from the predictions of the theory were observed, showing the need to add terms modifying the Laplace pressure force.

ISSN:1070-6631    

DOI:10.1063/1.868072

出版商:AIP    

年代:1994

数据来源: AIP

摘要:

Nonlinear evolution of two interacting modes of the Marangoni convection, a long‐scale deformational mode and a short‐scale stationary convective pattern, is considered. It is shown that the interaction between modes stabilizes surface deformation and leads to formation of various convective structures: stationary long‐scale modulated roll patterns, traveling and standing long waves, and can also cause chaotic convection (interfacial turbulence).

ISSN:1070-6631    

DOI:10.1063/1.868090

出版商:AIP    

年代:1994

数据来源: AIP

摘要:

Two‐dimensional Boussinesq convection is studied numerically using two different methods: a filtered pseudospectral method and a high‐order accurateenoscheme. The issue whether finite time singularity occurs for initially smooth flows is investigated. In contrast to the findings of Pumir and Siggia who reported finite time collapse of the bubble cap, the present numerical results suggest that the strain rate corresponding to the intensification of the density gradient across the front saturates at the bubble cap. Consequently, the thickness of the bubble decreases exponentially. On the other hand, the bubble experiences much stronger straining and intensification of gradients at its side. As the bubble rises, a secondary front also forms from its tail. Together with the primary front, they constitute a pair of tightly bound plus and minus double vortex sheet structure which is highly unstable and vulnerable to viscous dissipation.

ISSN:1070-6631    

DOI:10.1063/1.868044

出版商:AIP    

年代:1994

数据来源: AIP

摘要:

This paper considers the onset of double diffusive natural convection in a vertical layer of a binary fluid submitted to horizontal thermal and compositional gradients. The analysis deals with the particular situation where the resulting buoyancy forces (the Grashof numbers corresponding to the thermal and solutal effects) are opposing and of equal intensity. The stability analysis for the infinite layer shows that the purely diffusive (motionless) solution prevails at moderate Grashof numbers, and an analytical expression of the critical Rayleigh number as a function of the Lewis number is obtained. These results are then compared to the critical values which are determined from numerical simulations in an enclosure. Numerical calculations in the transient regime are used to give an interpretation of the stability of the steady state diffusive regime when the buoyancy forces are below the critical value.

ISSN:1070-6631    

DOI:10.1063/1.868045

出版商:AIP    

年代:1994

数据来源: AIP

摘要:

Shear flow over a plane wall that contains an axisymmetric depression or pore is studied using a new boundary integral method which is suitable for computing three‐dimensional Stokes flow within axisymmetric domains. Numerical results are presented for cavities in the shape of a section of a sphere or a circular cylinder of finite length, and for a family of pores or orifices with finite thickness. The results illustrate the distribution of shear stresses over the plane wall and inside the cavities or pores. It is found that in most cases, the distribution of shear stresses over the plane wall, around the depressions, is well approximated with that for flow over an orifice of infinitesimal thickness for which an exact solution is available. The kinematic structure of the flow is discussed with reference to eddy formation and three‐dimensional flow reversal. It is shown that the thickness of a circular orifice or depth of a pore play an important role in determining the kinematical structure of the flow underneath the orifice in the lower half‐space.  

ISSN:1070-6631    

DOI:10.1063/1.868046

出版商:AIP    

年代:1994

数据来源: AIP