摘要:

A new rotation symmetry for steady Hele–Shaw flows is reported. In the case when surface tension is neglected, it is shown that if a curveCmoving with constant velocityUis a solution to the Hele–Shaw problem, then the curveC˜ obtained from a rotation ofCabout its center by an arbitrary angle is also a solution with thesamevelocityU. Similar results hold for the case with surface tension if and only if the Schwarz function of the curveCis regular in the fluid region and at most a linear function at infinity. Several examples in which this principle is used to generate new solutions to the problem are also discussed.  

ISSN:0899-8213    

DOI:10.1063/1.858811

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

The two‐dimensional oscillatory flow around a circular cylinder is analyzed by means of the numerical approach described in Justesen [J. Fluid Mech.222, 157 (1991)]. For a fixed value of the ratio between the Stokes viscous thickness and the radius of the cylinder section, when the Reynolds number assumes low values, the flow is periodic and symmetric with respect to an axis aligned with the flow direction and crossing the axis of the cylinder. An increase in the Reynolds number beyond a first critical value causes the flow to bifurcate: the velocity field loses its spatial symmetry even though it retains its time periodicity. When the Reynolds number is larger than a second critical value, a new frequency appears in the flow. This new frequency, which is much smaller than the frequency of the basic flow, increases for increasing values of the Reynolds number till a phase locking takes place. A further increase in the Reynolds number leads the flow to a chaotic status. The ‘‘quasiperiodicity and phase locking’’ route to chaos can be recognized.

ISSN:0899-8213    

DOI:10.1063/1.858886

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

The evolution of short gravity waves on long gravity waves on the surface of deep water is studied. Both wave trains are assumed to be irrotational, mild in slope, and slowly modulated in space and time, but their scales are so different that the short wavelength is very much less than the long‐wave amplitude. Here, it is shown that the use of Lagrangian instead of the usual Eulerian coordinates is advantageous for yielding analytical results. Linear and nonlinear evolutions of short waves over intermediate and very long distances are discussed.

ISSN:0899-8213    

DOI:10.1063/1.858812

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

An expanding spherical gas bubble moves in an incompressible, viscous fluid under gravity. The nonlinear equations of motion are solved numerically. The growth of the radius of the bubble, the velocity of its center, and the drag experienced by the bubble are obtained with the progress of time. The gravity is found to influence the results significantly.  

ISSN:0899-8213    

DOI:10.1063/1.858813

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

The behavior of evaporating small diameter jets in a low‐pressure environment is studied experimentally. Charged coupled device (CCD) cameras connected to a computerized data logging system are employed for high‐speed imaging. Experiments at different jet velocities and environmental pressures have been performed with pure ether and ethanol, and also the mixtures of the two. Complex instability structures during the evaporation of the jet were observed. The recorded experimental evidences of these structures are presented and discussed.  

ISSN:0899-8213    

DOI:10.1063/1.858814

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

The linear stability of a modulated Taylor–Couette system when the inner cylindrical boundary consists of a crystalline solid‐liquid interface is considered. Both experimentally and in numerical calculations it is found that the two‐phase system is significantly less stable than the analogous rigid‐walled system for materials with moderately large Prandtl numbers. A numerical treatment based on Floquet theory is described, which gives results that are in good agreement with preliminary experimental findings. In addition, this instability is further examined by carrying out a formal asymptotic expansion of the solution in the limit of large Prandtl number. In this limit the Floquet analysis is considerably simplified, and the linear stability of the modulated system can be determined to leading order through a conventional stability analysis, without recourse to Floquet theory. The resulting simplified problem is then studied for both the narrow gap geometry and for the case of a finite gap. It is surprising that the determination of the linear stability of the two‐phase system is considerably simpler than that of the rigid‐walled system, despite the complications introduced by the presence of the crystal‐melt interface.

ISSN:0899-8213    

DOI:10.1063/1.858815

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

Computation of three‐dimensional (3‐D) Rayleigh–Taylor instability in compressible fluids is performed on a MIMD computer. A second‐order TVD scheme is applied with a fully parallelized algorithm to the 3‐D Euler equations. The computational program is implemented for a 3‐D study of bubble evolution in the Rayleigh–Taylor instability with varying bubble aspect ratio and for large‐scale simulation of a 3‐D random fluid interface. The numerical solution is compared with the experimental results by Taylor.

ISSN:0899-8213    

DOI:10.1063/1.858816

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

Thermocapillary convection is studied in two immiscible liquid layers with one free surface, one liquid/liquid interface, and differential heating applied parallel to the interfaces. An analytical solution is introduced for infinite horizontal layers. The defining parameter for the flow pattern is &lgr;, the ratio of the temperature coefficient of the interfacial tension to that of the surface tension. Four different flow patterns exist under zero gravity conditions. ‘‘Halt’’ conditions which halt the fluid motion in the lower encapsulated liquid layer have been found. A numerical experiment is carried out to study effects of vertical end walls on the double layer convection in a two‐dimensional cavity. The halt condition obtained from the analytical study is found to be valid in the limit of small Reynolds numbers. The flow in the encapsulated liquid layer can be suppressed substantially.

ISSN:0899-8213    

DOI:10.1063/1.858817

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

Numerical calculations have been carried out of steady, symmetric, three‐dimensional modes of convection in internally heated, infinite Prandtl number, Boussinesq fluids at a Rayleigh number of 1.4×104in a spherical shell with inner/outer radius of 0.55 and in a 3×3×1 rectangular box. Multiple patterns of convection occur in both geometries. In the Cartesian geometry the patterns are dominated by cylindrical cold downflows and a broad hot upwelling. In the spherical geometry the patterns consist of cylindrical cold downwellings centered either at the vertices of a tetrahedron or the centers of the faces of a cube. The cold downflow cylinders are immersed in a background of upwelling within which there are cylindrical hot concentrations (plumes) and hot halos around the downflows. The forced hot upflow return plumes of internally heated spherical convection are fundamentally different from the buoyancy‐driven plumes of heated from below convection.

ISSN:0899-8213    

DOI:10.1063/1.858818

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

How to describe vorticity creation from a moving wall is a long standing problem. This paper discusses relevant issues at the fundamental level. First, it is shown that the concept of ‘‘vorticity flux due to wall acceleration’’ can be best understood by following fluid particles on the wall rather than observing the flow at fixed spatial points. This is of crucial importance when the time‐averaged flux is to be considered. The averaged flux has to be estimated in a wall‐fixed frame of reference (in which there is no flux due to wall acceleration at all); or, if an inertial frame of reference is used, the generalized Lagrangian mean (GLM) also gives the same result. Then, for some simple but typical configurations, the time‐averaged vorticity flux from a harmonically oscillating wall with finite amplitude is analyzed, without appealing to small perturbation. The main conclusion is that the wall oscillation will produce an additional mean vorticity flux (a fully nonlinear streaming effect), which is partially responsible for the mechanism of vortex flow control by waves. The results provide qualitative explanation for some experimentally and/or computationally observed phenomena.

ISSN:0899-8213    

DOI:10.1063/1.858819

出版商:AIP    

年代:1993

数据来源: AIP