摘要:

Laboratory and numerical experiments were conducted to quantitatively determine the modal structure of transient, nonaxisymmetric modes observed during the instability of an impulsively initiated circular‐Couette flow. The instability develops initially as an axisymmetric, Go¨rtler‐vortex state and persists ultimately as a steady, axisymmetric Taylor‐vortex state of different wavelength. The transition between these two states results from the instability of the Go¨rtler mode combined with the underlying developing swirl flow and is dominated by nonaxisymmetric modes. The laboratory experiments employed flow visualization coupled with digital video and image‐processing techniques; numerical experiments were performed using the spectral‐element code,nekton. ©1995 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868630

出版商:AIP    

年代:1995

数据来源: AIP

摘要:

The plane Couette flow, a shear flow linearly stable for all values of the Reynolds number,R, is experimentally studied. A finite amplitude perturbation, local in both time and space, is created in order to destabilize the flow. A critical amplitude,Ac(R), below which disturbances are not sustained is measured. Above this amplitude, a turbulent spot grows to a spatially‐bounded turbulent state, persistent over times long compared to its typical growth time. The critical amplitude,Ac(R), is seen to diverge whenRapproaches the nonlinear critical Reynolds numberRNL=325±5 from above. Below this value of the Reynolds number, no destabilization occurs with this kind of perturbation, whatever its amplitude. The divergent behavior on approachingRNLis characterized in terms of a power law. This result sheds light on the discrepancies previously observed between critical Reynolds number measurements. The spot is then analyzed in terms of its inside structure, spreading rates, as well as waves and velocity profiles close to the spot, in order to compare it to plane Poiseuille and boundary layer spots. The spot evolution appears to be very similar to that observed for the plane Poiseuille spot. It is shown that the growth of the plane Couette spot can be described by the mechanism of ‘‘growth by destabilization.’’ ©1995 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868631

出版商:AIP    

年代:1995

数据来源: AIP

摘要:

Laboratory experiments and numerical computations are conducted for plane channel flow with a streamwise‐periodic array of cylinders. Well‐ordered, globally stable flow states emerge from primary and secondary instabilities, in contrast with other wall‐bounded shear flows, where instability generally leads directly to turbulence. A two‐dimensional flow resembling Tollmien–Schlichting waves arises from a primary instability at a critical value of the Reynolds number,R1=130, more than 40 times smaller than for plane Poiseuille flow. The primary transition is shown to be a supercritical Hopf bifurcation arising from aconvectiveinstability. A numerical linear stability analysis is in quantitative agreement with the experimental observations, and a simple one‐dimensional model captures essential features of the primary transition. The secondary flow loses stability atR2≊160 to a tertiary flow, with a standing wave structure along the streamwise direction and a preferred wave number in the spanwise direction. This three‐dimensional flow remains stable for a range ofR, even though the structures resemble the initial stages of the breakdown to turbulence typically displayed by wall‐bounded shear flow. The results of a Floquet stability analysis for the onset of three‐dimensional flow are in partial agreement with experiment. ©1995 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868632

出版商:AIP    

年代:1995

数据来源: AIP

摘要:

Linear stability analysis of a liquid–vapor interface under adverse gravitational field and velocity streaming is considered. The liquid is assumed viscous, incompressible, and motionless over a vapor layer with a uniform horizontal velocity. It is shown that while the coupled viscosity‐phase change mechanism of former studies adds considerably to the stability of the Rayleigh–Taylor problem, it has a deleterious effect on the Kelvin–Helmholtz mode of stability. ©1995 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868633

出版商:AIP    

年代:1995

数据来源: AIP

摘要:

The temporal inertial instabilities of the Type I Long’s vortex for large values of the flow force,M, are explored. It is found that growth rates and wave speeds obtained numerically for the exact vortex profiles agree very well with those obtained for large‐Mprofiles found by asymptotic means. Agreement is excellent, so the large‐Mstructure and inertial instability modes of the Type I Long’s vortex are now well established. It is determined that the modes computed here are ring modes. Both exact and asymptotic solutions display a spurious instability mode, which vanishes for increased resolution. ©1995 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868634

出版商:AIP    

年代:1995

数据来源: AIP

摘要:

In this paper the viscous decay of dipolar vortex structures in a linearly stratified fluid is investigated experimentally, and a comparison of the experimental results with simple theoretical models is made. The dipoles are generated by a pulsed horizontal injection of fluid. In a related experimental study by Flo´r and van Heijst [J. Fluid Mech.279, 101 (1994)], it was shown that, after the emergence of the pancake‐shaped vortex structure, the flow is quasi‐two‐dimensional and decays due to the vertical diffusion of vorticity and entrainment of ambient irrotational fluid. This results in an expansion of the vortex structure. Two decay models with the horizontal flow based on the viscously decaying Lamb–Chaplygin dipole, are presented. In a first model, the thickness and radius of the dipole are assumed constant, and in a second model also the increasing thickness of the vortex structure is taken into account. The models are compared with experimental data obtained from flow visualizations and from digital analysis of particle‐streak photographs. Although both models neglect entrainment and the decay is modeled by diffusion only, a reasonable agreement with the experiments is obtained. ©1995 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868635

出版商:AIP    

年代:1995

数据来源: AIP

摘要:

The existence of steadily translating vortices in a semi‐infinite barotropic fluid stratified by a constant gravitational field is considered. Assuming that the flow field of the vortex is subsonic and contains finite total kinetic energy, it is found that steadily translating vortices do not exist in three dimensions, but do exist in two dimensions. An analogy between a subsonic, barotropic, stratified fluid, and a uniform fluid with a free‐slip planar boundary is exploited to show that the same result applies in a semi‐infinite uniform fluid. ©1995 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868636

出版商:AIP    

年代:1995

数据来源: AIP

摘要:

The forces that act on bubbles as they are entrained by a vortex are measured using particle image velocimetry. Triple exposure images are used to measure the velocity and acceleration of the fluid and the bubbles simultaneously. Distinction between phases is achieved by using fluorescent particles as liquid flow tracers. The buoyancy, pressure, and inertia forces are computed from the data, while the drag and the lift forces are determined from a force balance on each bubble. It is found that in the present range of bubble diameters, 500 &mgr;m<d<800 &mgr;m, and Reynolds numbers, 20<Re<80, the drag on a bubble is similar to that on a solid body. Vorticity does not have a significant effect on the drag coefficient. The lift coefficients are significantly higher than currently available analytical and numerical estimates. The coefficients are independent of the Reynolds number and are proportional to the fourth root of the local vorticity. Estimates of the Bassett force show that it can be neglected in the present experiment. Computed bubble trajectories, based on the measured lift and drag coefficients, compare well with experimental observations. ©1995 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868637

出版商:AIP    

年代:1995

数据来源: AIP

摘要:

This paper presents a linear stability analysis as well as some numerical results for the motion of heavy particles in the flow field of a Burgers vortex, under the combined effects of particle inertia, Stokes drag, and gravity. By rendering the particle motion equations dimensionless, the particle Stokes number, a Froude number, and a vortex Reynolds number are obtained as the governing three parameters. In the absence of gravity, the vortex center represents a stable equilibrium point for particles up to a critical value of the Stokes number, as the inward drag overcomes the destabilizing centrifugal force on the particle. Particles exceeding the critical Stokes number value asymptotically approach closed circular orbits. Under the influence of gravity, one or three equilibrium points appear away from the vortex center. Both their locations and their stability characteristics are derived analytically. These stability characteristics can furthermore be related to the nature of the critical points in a related directional force field. These findings are expected to be applicable to the coupling between the small‐scale turbulent flow structures and the motion of suspended particles. ©1995 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868778

出版商:AIP    

年代:1995

数据来源: AIP

摘要:

Three‐dimensional Euler equations are studied numerically and analytically to characterize intense vortex stretching in an inviscid fluid. Emphasis is put on the nonlocal effects stemming from the pressure term. The purpose of this paper is twofold. One is to give numerically a detailed characterization of vortex structures on the basis of previously proposed two eigenvalue problems associated with vorticity. The other is to give some mathematical analyses which highlight the role of the pressure Hessian in vortex dynamics, especially in connection with a possible singularity. Also discussed are the differences in local and global (possible) blowups. The blowup problem is not directly discussed by the present numerics at moderate resolution. ©1995 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868638

出版商:AIP    

年代:1995

数据来源: AIP