摘要:

Present numerical simulations of the transition scenario of a rotating fluid flow in a closed cylinder are presented, where the motion is created by a rotating lid. The numerical algorithm, which is based on a finite‐difference discretization of the axisymmetric Navier‐Stokes equations, is validated against experimental visualizations of both transient and stable periodic flows. The complexity of the flow problem is illuminated numerically by injecting flow tracers into the flow domain and following their evolution in time. The vortex dynamics appears as stretching, folding and squeezing of flow structures which wave along the contour of a central vortex core. The main purpose of the study is to clarify the mechanisms of the transition scenario and relate these to experiences known from other dynamical systems and bifurcation theory. The dynamical system was observed to exhibit up to three multiple solutions for the same Reynolds number, and to contain four discernible branches. The transition to strange attractor behavior was identified as a nontrivial Ruelle‐Takens transition through a transient torus. The various solution branches of the rotating flow problem are illustrated by phase portraits and summarized on a frequency diagram. ©1995 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868600

出版商:AIP    

年代:1995

数据来源: AIP

摘要:

The transition of the cylinder wake is investigated experimentally in a water channel and is computed numerically using a finite‐difference scheme. Four physically different instabilities are observed: a local ‘‘vortex‐adhesion mode,’’ and three near‐wake instabilities, which are associated with three different spanwise wavelengths of approximately 1, 2, and 4 diam. All four instability processes can originate in a narrow Reynolds‐number interval between 160 and 230, and may give rise to different transition scenarios. Thus, Williamson’s [Phys. Fluids31, 3165 (1988)] experimental observation of a hard transition is for the first time numerically reproduced, and is found to be induced by the vortex‐adhesion mode. Without vortex adhesion, a soft onset of three‐dimensionality is numerically and experimentally obtained. A control‐wire technique is proposed, which suppresses transition up to a Reynolds number of 230. ©1995 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868601

出版商:AIP    

年代:1995

数据来源: AIP

摘要:

Unsteady evolutions of vortex rings with linearly distributed vorticity and various core parameters are considered in an unbounded, inviscid fluid. The instability of a Norbury vortex with a moderate core thickness parameter &agr; is also investigated. Contour integral expressions based on the Biot–Savart law for the velocity field induced by a vortex ring are derived. Numerical results show that all vortex rings except the Norbury vortices will undergo an unsteady evolution process to reach an asymptotic state. The process may be roughly divided into two major stages: initial large deformation stage and later asymptotic oscillating stage. Vortex filamentation is often observed during the first stage. In the second stage, the vortex oscillates periodically with nearly constant amplitude; its core closely resembles a Norbury vortex having the same circulation and impulse, but the dynamic properties and kinetic energies are different. ©1995 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868602

出版商:AIP    

年代:1995

数据来源: AIP

摘要:

Motion of a free point vortex near a circular cylinder in a uniform oncoming flow is considered. There is a point at which the point vortex velocity is zero. This stationary position is unstable. Introducing two periodic point sources of zero mean flow rate modifies the point vortex velocity field so that instead of the stationary position there is a periodic trajectory. The corresponding periodic motion of the vortex is found to be stable over a certain range of characteristics of periodic blowing/suction modeled with periodic sources. In particular, for stabilization the amplitude of the source flow rate oscillations must not exceed a certain limit. The results are believed to bear on the problem of enhancing lift at high angle of attack with the use of trapped vortices. ©1995 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868603

出版商:AIP    

年代:1995

数据来源: AIP

摘要:

The problem of the diffusion of two counter‐rotating vortices of equal strength is studied numerically and analytically. Asymptotic expansions are derived for the limiting behavior of the solution for small times, for small Reynolds numbers, and for large times. The results are used to more fully understand the drift and decay of the vortex system. Thus it is shown that different measures for the position of the vortex system used by previous authors may give significantly different values for the drift velocity of the vortices. The expansion for small Reynolds number shows that these differences remain even in the Stokes limit Re→0, in which the vorticity system becomes symmetric about the line connecting the vortex centers. But surprisingly, the large time expansion shows that for large times all drift velocities become identical. Moreover, this universal velocity is different from the average velocity in each half plane although it equals the velocity of the centers of vorticity of those planes. The small time expansion shows that increasing Reynolds number makes the vortices more symmetric. This tends to reduce the differences between the drift velocities. The small time expansion describes the numerical solution well as long as the vortices remain small compared to their spacing. The numerical results show that the Stokes solution describes various flow quantities fairly well for Reynolds numbers up to 600 based on the circulation; however, nonzero Reynolds number reduces the decay of the circulation of the vortices even on a diffusive time scale. ©1995 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868604

出版商:AIP    

年代:1995

数据来源: AIP

摘要:

The stability of a flat plate boundary layer modulated by stationary streamwise vortices was studied experimentally in the T‐324 low speed wind tunnel in Novosibirsk. Vortices were generated inside the boundary layer by means of roughness elements arranged in a regular array along the spanwise (z‐) direction. Transition is not caused directly by these structures, but by the growth of small amplitude traveling waves riding on top of the steady vortices. This situation is analogous to the transition process in Go¨rtler and cross‐flows. The waves were found to amplify up to a stage where higher harmonics are generated, leading to turbulent breakdown and disintegration of the spanwise boundary layer structure. For strong modulations, the observed instability is quite powerful, and can be excited ‘‘naturally’’ by small uncontrollable background disturbances. Controlled oscillations were then introduced by means of a vibrating ribbon, allowing a detailed investigation of the wave characteristics. The instability seems to be associated with the spanwise gradients of the mean flow, ∂U/∂z, and at allz‐positions, the maximum wave amplitude was found at a wall‐normal position where the mean velocity is equal to the phase velocity of the wave,U(y)=c, i.e., at the local critical layer. Unstable waves were observed at frequencies well above those for which Tollmien–Schlichting (TS) waves amplify in the Blasius boundary layer. Excitation at lower frequencies and milder basic flow modulations showed that TS‐type waves may also develop. The relation between TS‐type waves and the observed high‐frequency instability is discussed in the light of previous authors’ findings. ©1995 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868605

出版商:AIP    

年代:1995

数据来源: AIP

摘要:

A simple model in three real dimensions is proposed, illustrating a possible mechanism of transition to turbulence. The linear part of the model is stable but highly non‐normal, so that certain inputs experience a great deal of growth before they eventually decay. The nonlinear terms of the model contribute no energy growth, but recycle some of the linear outputs into inputs, closing a feedback loop and allowing initially small solutions to ‘‘bootstrap’’ to a much larger amplitude. Although different choices of parameters in the nonlinearity lead to a variety of long‐term behaviors, the bootstrapping process is essentially independent of the details of the nonlinearity and varies predictably with the Reynolds number. The bootstrapping scenario demonstrated by this model is the basis of some recent explanations for the failure of classical hydrodynamic stability analysis to predict the onset of turbulence in certain flow configurations. ©1995 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868606

出版商:AIP    

年代:1995

数据来源: AIP

摘要:

Most applications of the dynamic subgrid‐scale stress model use volume‐ or planar‐averaging to avoid ill‐conditioning of the model coefficient, which may result in numerical instabilities. Furthermore, a spatially‐varying coefficient is mathematically inconsistent with the original derivation of the model. A localization procedure is proposed here that removes the mathematical inconsistency to any desired order of accuracy in time. This model is applied to the simulation of rotating channel flow, and results in improved prediction of the turbulence statistics. The model coefficient vanishes in regions of quiescent flow, reproducing accurately the intermittent character of the flow on the stable side of the channel. Large‐scale longitudinal vortices can be identified, consistent with the observation from experiments and direct simulations. The effect of the unresolved scales on higher‐order statistics is also discussed. ©1995 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868607

出版商:AIP    

年代:1995

数据来源: AIP

摘要:

Pressure spectra at large wave numbers are calculated for Lundgren–Townsend vortex models of the fine scales of homogeneous turbulence. Specific results are given for the Burgers vortex and also for the Lundgren‐strained spiral vortex. For the latter case, it is found that the contribution to the shell‐summed spectrum produced by the interaction between the axisymmetric and nonaxisymmetric components of the velocity field is proportional tok−7/3(k=‖k‖ is the modulus of the wave number) in agreement with Kolmogorov‐type dimensional arguments. Numerical estimates of the dimensionless prefactors for this component are obtained in Kolmogorov scaling variables and comparisons are made with results from the Batchelor–Kolmogorov theory, and with experimental measurement. ©1995 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868608

出版商:AIP    

年代:1995

数据来源: AIP

摘要:

Plan view flow visualization experiments were conducted in the atmospheric surface layer that flows over the Great Salt Lake Desert at the U.S. Army Dugway Proving Ground, Dugway, Utah. Measurements were acquired on a nonconductive, polyethylene platform made flush with the desert floor. Surface conditions upstream of the measurement site were flat, devoid of vegetation, and because of the dried mud/clay/salt composition, essentially dust free. Local surface variations ranged between 1 and 3 mm, which corresponded to three to ten viscous units during the experiments. Flow visualizations were accomplished by continuously injecting theatrical fog through a tangential slit covering a smoke reservoir buried under the platform. During the visualizations, the atmospheric surface layer flow was near neutral thermal stability. Flow velocities at 2.0 m above the surface maintained directional constancy, with a magnitude of about 1.5 m/s. A single element hot‐wire probe positioned neary+=3.4 was used to measure the wall shear. Visualization results indicate the existence of the pocket and streak motions seen at much lower Reynolds number. The average inner normalized streak spacing was found to be &lgr;+=93.1, with a positively skewed, nearly lognormal distribution. The average maximum inner normalized pocket width was found to bew+=127.2, with a positively skewed distribution. The average time between pockets was determined to beT+=36.6. Comparisons are made with existing low Reynolds number results, and a brief discussion is provided regarding the physics underlying the present observations. ©1995 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868763

出版商:AIP    

年代:1995

数据来源: AIP