Scaling in three-dimensional and quasi-two-dimensional rotating turbulent flows

2003 ◽  
Vol 15 (8) ◽  
pp. 2091-2104 ◽  
Author(s):  
Charles N. Baroud ◽  
Brendan B. Plapp ◽  
Harry L. Swinney ◽  
Zhen-Su She
Keyword(s):  
Turbulent Flows ◽  
Three Dimensional ◽  
Two Dimensional

scholarly journals Turbulent 2.5-dimensional dynamos

2016 ◽  
Vol 799 ◽  
pp. 246-264 ◽  
Author(s):  
K. Seshasayanan ◽  
A. Alexakis
Keyword(s):  
Turbulent Flows ◽  
Large Scale ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Wide Range ◽  
Two Dimensional Flow

We study the linear stage of the dynamo instability of a turbulent two-dimensional flow with three components $(u(x,y,t),v(x,y,t),w(x,y,t))$ that is sometimes referred to as a 2.5-dimensional (2.5-D) flow. The flow evolves based on the two-dimensional Navier–Stokes equations in the presence of a large-scale drag force that leads to the steady state of a turbulent inverse cascade. These flows provide an approximation to very fast rotating flows often observed in nature. The low dimensionality of the system allows for the realization of a large number of numerical simulations and thus the investigation of a wide range of fluid Reynolds numbers $Re$, magnetic Reynolds numbers $Rm$ and forcing length scales. This allows for the examination of dynamo properties at different limits that cannot be achieved with three-dimensional simulations. We examine dynamos for both large and small magnetic Prandtl-number turbulent flows $Pm=Rm/Re$, close to and away from the dynamo onset, as well as dynamos in the presence of scale separation. In particular, we determine the properties of the dynamo onset as a function of $Re$ and the asymptotic behaviour in the large $Rm$ limit. We are thus able to give a complete description of the dynamo properties of these turbulent 2.5-D flows.

scholarly journals Kazantsev model in non-helical 2.5-dimensional flows

2016 ◽  
Vol 806 ◽  
pp. 627-648 ◽  
Author(s):  
K. Seshasayanan ◽  
A. Alexakis
Keyword(s):  
Turbulent Flows ◽  
Three Dimensional ◽  
Analytical Calculation ◽  
Reynolds Numbers ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Control Parameters ◽  
Governing Equations ◽  
Field Correlation ◽  
Good Agreement

We study the dynamo instability for a Kazantsev–Kraichnan flow with three velocity components that depend only on two dimensions $\boldsymbol{u}=(u(x,y,t),v(x,y,t),w(x,y,t))$ often referred to as 2.5-dimensional (2.5-D) flow. Within the Kazantsev–Kraichnan framework we derive the governing equations for the second-order magnetic field correlation function and examine the growth rate of the dynamo instability as a function of the control parameters of the system. In particular we investigate the dynamo behaviour for large magnetic Reynolds numbers $Rm$ and flows close to being two-dimensional and show that these two limiting procedures do not commute. The energy spectra of the unstable modes are derived analytically and lead to power-law behaviour that differs from the three-dimensional and two-dimensional cases. The results of our analytical calculation are compared with the results of numerical simulations of dynamos driven by prescribed fluctuating flows as well as freely evolving turbulent flows, showing good agreement.

Quantitative three-dimensional imaging and the structure of passive scalar fields in fully turbulent flows

1990 ◽  
Vol 216 ◽  
pp. 1-34 ◽  
Author(s):  
Rahul R. Prasad ◽  
K. R. Sreenivasan
Keyword(s):  
Turbulent Flows ◽  
Three Dimensional ◽  
Scalar Fields ◽  
Passive Scalar ◽  
Working Fluid ◽  
Small Scale ◽  
Main Body ◽  
Two Dimensional ◽  
Scaling Properties ◽  
Two Dimensional Images

The three-dimensional turbulent field of a passive scalar has been mapped quantitatively by obtaining, effectively instantaneously, several closely spaced parallel two-dimensional images; the two-dimensional images themselves have been obtained by laser-induced fluorescence. Turbulent jets and wakes at moderate Reynolds numbers are used as examples. The working fluid is water. The spatial resolution of the measurements is about four Kolmogorov scales. The first contribution of this work concerns the three-dimensional nature of the boundary of the scalar-marked regions (the ‘scalar interface’). It is concluded that interface regions detached from the main body are exceptional occurrences (if at all), and that in spite of the large structure, the randomness associated with small-scale convolutions of the interface are strong enough that any two intersections of it by parallel planes are essentially uncorrelated even if the separation distances are no more than a few Kolmogorov scales. The fractal dimension of the interface is determined directly by box-counting in three dimensions, and the value of 2.35 ± 0.04 is shown to be in good agreement with that previously inferred from two-dimensional sections. This justifies the use of the method of intersections. The second contribution involves the joint statistics of the scalar field and the quantity χ* (or its components), χ* being the appropriate approximation to the scalar ‘dissipation’ field in the inertial–convective range of scales. The third aspect relates to the multifractal scaling properties of the spatial intermittency of χ*; since all three components of χ* have been obtained effectively simultaneously, inferences concerning the scaling properties of the individual components and their sum have been possible. The usefulness of the multifractal approach for describing highly intermittent distributions of χ* and its components is explored by measuring the so-called singularity spectrum (or the f(α)-curve) which quantifies the spatial distribution of various strengths of χ*. Also obtained is a time sequence of two-dimensional images with the temporal resolution on the order of a few Batchelor timescales; this enables us to infer features of temporal intermittency in turbulent flows, and qualitatively the propagation speeds of the scalar interface. Finally, a few issues relating to the resolution effects have been addressed briefly by making point measurements with the spatial and temporal resolutions comparable with the Batchelor lengthscale and the corresponding timescale.

Use of the mixing length concept to correctly reproduce velocity profiles of turbulent flows

1998 ◽  
Vol 25 (2) ◽  
pp. 232-240 ◽  
Author(s):  
Jean-Loup Robert ◽  
Mohamed Khelifi ◽  
Ahmed Ghanmi
Keyword(s):  
Turbulent Flows ◽  
Turbulent Viscosity ◽  
Three Dimensional ◽  
Velocity Profiles ◽  
Point Of View ◽  
The Other ◽  
Mixing Length ◽  
Two Dimensional ◽  
Constant Viscosity ◽  
Good Agreement

Since the viscous analogy of turbulence was introduced by Reynolds, many formulations for turbulent viscosity have been proposed. One of them, based on the mixing length concept, is investigated here in a broader point of view. The mixing length concept was used to correctly model turbulent velocity profiles for irregular two-dimensional and three-dimensional domains. Two cases of study were investigated for this purpose: a simple two-dimensional aerodynamic problem and a more complicated three-dimensional hydraulic problem. Results showed that the use of a constant viscosity fails to correctly reproduce experimental observations. On the other hand, the use of the mixing length concept leads to a good agreement between the measured and predicted values.Key words: fluid flow, finite element method, mixing length flow theory, turbulent flow, velocity profiles.

Experimental characterization of viscoelastic effects on two- and three-dimensional shear instabilities

2000 ◽  
Vol 416 ◽  
pp. 151-172 ◽  
Author(s):  
OLIVIER CADOT ◽  
SATISH KUMAR
Keyword(s):  
Turbulent Flows ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Experimental Characterization ◽  
Elastic Forces ◽  
Viscoelastic Effects ◽  
Karman Street ◽  
Dimensional Instability ◽  
Elasticity Number

Instabilities of a wake produced by a circular cylinder in a uniform water flow are studied experimentally when viscoelastic solutions are injected through holes pierced in the cylinder. It is shown that the viscoelastic solutions fill the shear regions and drastically modify the instabilities. The two-dimensional instability giving rise to the Kármán street is found to be inhibited: the roll-up process appears to be delayed and the wavelength of the street increases. The wavelength increase obeys an exponential law and depends on the elasticity number, which provides a ratio of elastic forces to inertial forces. The three-dimensional instability leading to the A mode is generally found to be suppressed. In the rare case where the A mode is observed, its wavelength is shown to be proportional to the wavelength of the Kármán street and the streamwise stretching appears to be inhibited. Injection of viscoelastic solutions also decreases the aspect ratio of the two-dimensional wake, and this is correlated with stabilization of the A mode and with changes in the shape of the Kármán vortices. The observations of this work are consistent with recent numerical simulations of viscoelastic mixing layers. The results suggest mechanisms through which polymers inhibit the formation of high-vorticity coherent structures and reduce drag in turbulent flows.

scholarly journals Non-local energy transfers in rotating turbulence at intermediate Rossby number

2011 ◽  
Vol 690 ◽  
pp. 129-147 ◽  
Author(s):  
L. Bourouiba ◽  
D. N. Straub ◽  
M. L. Waite
Keyword(s):  
Turbulent Flows ◽  
Scaling Law ◽  
Three Dimensional ◽  
Rossby Number ◽  
Local Energy ◽  
Two Dimensional ◽  
Horizontal Scale ◽  
Energy Transfers ◽  
Non Local ◽  
Non Locality

AbstractTurbulent flows subject to solid-body rotation are known to generate steep energy spectra and two-dimensional columnar vortices. The localness of the dominant energy transfers responsible for the accumulation of the energy in the two-dimensional columnar vortices of large horizontal scale remains undetermined. Here, we investigate the scale-locality of the energy transfers directly contributing to the growth of the two-dimensional columnar structures observed in the intermediate Rossby number ($\mathit{Ro}$) regime. Our approach is to investigate the dynamics of the waves and vortices separately: we ensure that the two-dimensional columnar structures are not directly forced so that the vortices can result only from association with wave to vortical energy transfers. Detailed energy transfers between waves and vortices are computed as a function of scale, allowing the direct tracking of the role and scales of the wave–vortex nonlinear interactions in the accumulation of energy in the large two-dimensional columnar structures. It is shown that the dominant energy transfers responsible for the generation of a steep two-dimensional spectrum involve direct non-local energy transfers from small-frequency small-horizontal-scale three-dimensional waves to large-horizontal-scale two-dimensional columnar vortices. Sensitivity of the results to changes in resolution and forcing scales is investigated and the non-locality of the dominant energy transfers leading to the emergence of the columnar vortices is shown to be robust. The interpretation of the scaling law observed in rotating flows in the intermediate-$\mathit{Ro}$ regime is revisited in the light of this new finding of dominant non-locality.

Computational Fluid Dynamics and Heat Transfer Analysis for a Novel Heat Exchanger

2015 ◽  
Vol 137 (5) ◽  
Author(s):  
Haolin Ma ◽  
Dennis E. Oztekin ◽  
Seyfettin Bayraktar ◽  
Sedat Yayla ◽  
Alparslan Oztekin
Keyword(s):  
Heat Transfer ◽  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Heat Exchanger ◽  
Turbulent Flows ◽  
Flow Structure ◽  
Three Dimensional ◽  
Flow Characteristics ◽  
Heat Transfer Analysis ◽  
Two Dimensional

Computational fluid dynamics (CFD) and heat transfer simulations are conducted for a novel heat exchanger. The heat exchanger consists of semi-circle cross-sectioned tubes that create narrow slots oriented in the streamwise direction. Numerical simulations are conducted for Reynolds numbers (Re) ranging from 700 to 30,000. Three-dimensional turbulent flows and heat transfer characteristics in the tube bank region are modeled by the k-ε Reynolds-averaged Navier–Stokes (RANS) method. The flow structure predicted by the two-dimensional and three-dimensional simulations is compared against that observed by the particle image velocimetry (PIV) for Re of 1500 and 4000. The adequate agreement between the predicted and observed flow characteristics validates the numerical method and the turbulent model employed here. The three-dimensional and the two-dimensional steady flow simulations are compared to determine the effects of the wall on the flow structure. The wall influences the spatial structure of the vortices formed in the wake of the tubes and near the exit of the slots. The heat transfer coefficient of the slotted tubes improved by more than 40% compare to the traditional nonslotted tubes.

Stability analysis and large-eddy simulation of rotating turbulence with organized eddies

1994 ◽  
Vol 278 ◽  
pp. 175-200 ◽  
Author(s):  
Claude Cambon ◽  
Jean-Pierre Benoit ◽  
Liang Shao ◽  
Laurent Jacquin
Keyword(s):  
Large Eddy Simulation ◽  
Turbulent Flows ◽  
Pure Shear ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Eddy Simulation ◽  
Rotating Turbulence ◽  
Special Cases ◽  
Large Eddy ◽  
The Stability

Rotation strongly affects the stability of turbulent flows in the presence of large eddies. In this paper, we examine the applicability of the classic Bradshaw-Richardson criterion to flows more general than a simple combination of rotation and pure shear. Two approaches are used. Firstly the linearized theory is applied to a class of rotating two-dimensional flows having arbitrary rates of strain and vorticity and streamfunctions that are quadratic. This class includes simple shear and elliptic flows as special cases. Secondly, we describe a large-eddy simulation of initially quasi-homogeneous three-dimensional turbulence superimposed on a periodic array of two-dimensional Taylor-Green vortices in a rotating frame.The results of both approaches indicate that, for a large structure of vorticity W and subject to rotation Ω, maximum destabilization is obtained for zero tilting vorticity (½W + 2Ω = 0) whereas stability occurs for zero absolute vorticity (2Ω = 0) These results are consistent with the Bradshaw-Richardson criterion; however the numerical results show that in other cases the Bradshaw-Richardson number $B=2\Omega(W+2\Omega)/W^2$ is not always a good indicator of the flow stability.

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