摘要:

Several situations have been studied in which a fluid–vapor or fluid–fluid interface ruptures, using molecular dynamics simulations of 3000 to 20 000 Lennard‐Jones molecules in three dimensions. The cases studied are the Rayleigh instability of a liquid thread, the burst of a liquid drop immersed in a second liquid undergoing shear, and the rupture of a liquid sheet in an extensional flow. The late stages of the rupture process involve the gradual withdrawal of molecules from a thinning neck, or the appearance and growth of holes in a sheet. In all cases, it is found that despite the small size of the systems studied, tens of angstroms, the dynamics is in at least qualitative accord with the behavior expected from continuum calculations, and in some cases the agreement is to within tens of percent. Remarkably, this agreement occurs even though the Eulerian velocity and stress fields are essentially unmeasurable—dominated by thermal noise. The limitations and prospects for such molecular simulation techniques are assessed.

ISSN:0899-8213    

DOI:10.1063/1.858879

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

When a bubble translates, the resulting motion of the interface causes interfacial energy to be convected from the front to the back of the bubble. In the front regions, this convection causes the interface to cool until conduction from the bulk can balance the removal of interfacial energy, while analogous heating occurs at the rear locations; therefore, the motion induces a temperature gradient around the bubble. It is predicted that these microscale effects can add to yield macroscopic temperature gradients and energy fluxes in swarms of moving bubbles. The extent to which the temperature gradient across a single bubble changes the migration velocity by inducing interfacial tension gradients is also considered; the calculations reveal this effect to be significant for low viscosity liquids such as liquid CO2and most liquids, including water, at elevated temperatures.

ISSN:0899-8213    

DOI:10.1063/1.858880

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

Filtration using large pressures is an effective method for removing liquids from a flocculated suspension and creating a high volume fraction filtercake. Recent experimental work exhibits phenomena that are unexplained by previous calculations with nonlinear models. These models are modified and now predict the region of clear liquid and the high concentration of the filtercake observed in filtration at large pressure. The governing equations are based on the assumption that, at sufficiently high volume fractions, a network forms through the aggregation of flocs and possesses a compressive yield stressPy(&fgr;) that depends only on the local volume fraction &fgr;.

ISSN:0899-8213    

DOI:10.1063/1.858881

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

Perturbation methods are used to analyze the receptivity and early evolution of boundary‐layer instabilities over a wavy surface. The length scale for the surface variation is considered to be much smaller than the natural instability wavelength. This provides a simplified model for distributed roughness. Acoustic disturbances in the free stream couple with steady perturbations resulting from the waviness to force traveling‐wave modes. At first order, the disturbance field contains a Stokes mode resulting from the acoustic perturbation, and a pair of steady modes resulting from the surface variation. Interactions between these modes produce steady, unsteady, and traveling‐wave modes at second order. Further interactions, at third order, then produce a forcing that is close to resonance with the natural instabilities. The near‐resonant forcing provides for a distributed energy transfer into the natural‐instability eigenmode resulting in a nonlocalized receptivity. The total amplitude resulting from the receptivity shows an effective subcritical growth. Growth downstream of the neutral point is also increased. When the waviness has an abrupt beginning, the effective growth rates become very large. Results from the analysis show qualitative features that are observed in stability experiments for boundary layers over distributed roughness.

ISSN:0899-8213    

DOI:10.1063/1.858882

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

A numerical study of the inertial waves in an axisymmetric transcritical flow of rotating fluid passing through a long circular tube is described. The waves are excited either by an obstacle on the axis of the tube or by a local undulation of the tube wall. In all the calculations, the flow has a circulation of the Burgers‐vortex type. The solutions of the Navier–Stokes equations are compared with the solutions of the forced KdV (Korteweg–de Vries) equation and it is found that the waves that appear in the solutions of the Navier–Stokes equations are described, at least qualitatively, by the solutions of the forced KdV equation. In this study, the forced KdV equation that has also a cubic nonlinear term is derived. However, the effect of the cubic nonlinearity is found to be small, at least for the upstream circulation distribution used in this study.

ISSN:0899-8213    

DOI:10.1063/1.858883

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

The propagation of three‐dimensional small‐amplitude long waves on a vortex filament running down the center of a circular tube is investigated analytically. The vortex flow is idealized by an infinite concentrated potential vortex filament immersed in an axial uniform flow that is displaced from the axis of the tube by a small three‐dimensional perturbation. The rigid walls of the tube are represented by a potential surface source distribution that also has the nature of a small perturbation. A linearization of the flow‐field equations, with respect to the basic state of a straight filament along the tube axis, results in an eigenvalue problem. The analytical solution shows that the vortex in the center of the tube is stable and the disturbances propagate as constant amplitude displacement waves along the vortex line and as source‐intensity fluctuations along the inner surface of the tube wall. Two different basic modes of either a helical or rotating sinusoidal wave can propagate along the vortex filament. A ‘‘supercritical’’ state is defined by the characteristics of the flow in which waves can propagate only downstream. It is shown from available experimental data that vortex flows in tubes that experienced vortex breakdown farther downstream, were ‘‘supercritical’’ at the tube inlet.

ISSN:0899-8213    

DOI:10.1063/1.858884

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

The effect of axial pressure gradient in producing gradual changes in amplitude and wavelength of both axisymmetrical and helical waves on a vortex core is studied analytically using an idealized model of a vortex with uniform axial vorticity across the core in an unbounded space. Possible implications of the findings on the vortex breakdown phenomenon are also considered. In agreement with previous literature on the subject, the steady solution for a supercritical vortex flow in an adverse pressure gradient is found to become complex (and hence break down) at a certain critical point. The axisymmetric waves on the core obey a hyperbolic system of equations. An explicit solution of these equations for small‐amplitude axisymmetric waves indicates that the wave amplitude becomes unbounded at the critical point in the linear theory. An implicit nonlinear solution of these equations shows the formation of ‘‘shocks’’ along the core considerably upstream of the critical point, which seem to correspond to formation of bubble‐type vortex breakdowns. A solution is also obtained for evolution of long helical waves on a vortex core in the presence of an axial pressure gradient, and this solution is used to suggest an explanation for why the vortex breakdown at times adopts a bubble form while at other times it adopts a spiral form.

ISSN:0899-8213    

DOI:10.1063/1.858645

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

The action of weak, streamwise vortices on a plane, incompressible, steady mixing layer is examined in the large Reynolds number limit. The outer, inviscid region is bounded by a vortex sheet to which the viscous region is confined. It is shown that the local linear analysis becomes invalid at streamwise distancesO(&egr;−1), where &egr;≪1 is the cross‐flow amplitude, and a new nonlinear analysis is constructed for this region. Numerical solutions of the nonlinear problem show that the vortex sheet undergoes anO(1) change in position and that the solution is ultimately terminated by a breakdown in the numerical procedure. The corresponding viscous layer shows downstream thickening, but appears to remain well behaved up to the terminal location.

ISSN:0899-8213    

DOI:10.1063/1.858646

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

Decaying two‐dimensional turbulence is characterized by the emergence of coherent vortices, which subsequently dominate the evolution. The temporal scaling behavior of the flow is analyzed using a scaling theory, a long‐time integration of the fluid equations, and a dissipative, modified point‐vortex model that represents the turbulence as a system of interacting coherent structures. Good agreement is found in the behavior of average vortex properties, low‐order moments of the flow fields, and the form of self‐similar evolution.

ISSN:0899-8213    

DOI:10.1063/1.858647

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

The dynamics of tilted dipole vortices in the equivalent barotropic vorticity (or Hasegawa–Mima) equation is studied. A recent theory is compared with numerical simulations and found to describe the short time behavior of dipole vortices well. In the long time limit the dipoles are found to either disintegrate or relax toward a steady eastward propagating dipole vortex. This relaxation is a consequence of nonviscous enstrophy loss by the dipole vortex.

ISSN:0899-8213    

DOI:10.1063/1.858648

出版商:AIP    

年代:1993

数据来源: AIP