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.

Relative dispersion in generalized two-dimensional turbulence

2017 ◽  
Vol 821 ◽  
pp. 358-383 ◽  
Author(s):  
Alexis Foussard ◽  
Stefano Berti ◽  
Xavier Perrot ◽  
Guillaume Lapeyre
Keyword(s):  
Probability Distributions ◽  
Turbulence Models ◽  
Relative Displacement ◽  
Relative Dispersion ◽  
Spectral Energy ◽  
Two Dimensional ◽  
Energy Transfers ◽  
Non Local ◽  
Turbulent Cascade ◽  
Non Locality

The statistical properties of turbulent fluids depend on how local the energy transfers among scales are, i.e. whether the energy transfer at some given scale is due to the eddies at that particular scale, or to eddies at larger (non-local) scale. This locality in the energy transfers may have consequences for the relative dispersion of passive particles. In this paper, we consider a class of generalized two-dimensional flows (produced by the so-called $\unicode[STIX]{x1D6FC}$-turbulence models), theoretically possessing different properties in terms of locality of energy transfers. It encompasses the standard barotropic quasi-geostrophic (QG) and the surface quasi-geostrophic (SQG) models as limiting cases. The relative dispersion statistics are examined, both as a function of time and as a function of scale, and compared to predictions based on phenomenological arguments assuming the locality of the cascade. We find that the dispersion statistics follow the predicted values from local theories, as long as the parameter $\unicode[STIX]{x1D6FC}$ is small enough (dynamics close to that of the SQG model), for sufficiently small initial pair separations. In contrast, non-local dispersion is observed for the QG model, a robust result when looking at relative displacement probability distributions. However, we point out that spectral energy transfers do have a non-local contribution for models with different values of $\unicode[STIX]{x1D6FC}$, including the SQG case. This indicates that locality/non-locality of the turbulent cascade may not always imply locality/non-locality in the relative dispersion of particles and that the self-similar nature of the turbulent cascade is more appropriate for determining the relative dispersion locality.

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.

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

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.

Rotating free-shear flows. Part 2. Numerical simulations

1995 ◽  
Vol 293 ◽  
pp. 47-80 ◽  
Author(s):  
Olivier Métais ◽  
Carlos Flores ◽  
Shinichiro Yanase ◽  
James J. Riley ◽  
Marcel Lesieur
Keyword(s):  
Solid Body ◽  
Mixing Layer ◽  
Three Dimensional ◽  
Rossby Number ◽  
Two Dimensional ◽  
Body Rotation ◽  
Mean Flow ◽  
Hairpin Vortices ◽  
Solid Body Rotation ◽  
Rotation Rates

The three-dimensional dynamics of the coherent vortices in periodic planar mixing layers and in wakes subjected to solid-body rotation of axis parallel to the basic vorticity are investigated through direct (DNS) and large-eddy simulations (LES). Initially, the flow is forced by a weak random perturbation superposed on the basic shear, the perturbation being either quasi-two-dimensional (forced transition) or three-dimensional (natural transition). For an initial Rossby number Ro(i), based on the vorticity at the inflexion point, of small modulus, the effect of rotation is to always make the flow more two-dimensional, whatever the sense of rotation (cyclonic or anticyclonic). This is in agreement with the Taylor–Proudman theorem. In this case, the longitudinal vortices found in forced transition without rotation are suppressed.It is shown that, in a cyclonic mixing layer, rotation inhibits the growth of three-dimensional perturbations, whatever the value of the Rossby number. This inhibition exists also in the anticyclonic case for |Ro(i)| ≤ 1. At moderate anticyclonic rotation rates (Ro(i) < −1), the flow is strongly destabilized. Maximum destabilization is achieved for |Ro(i) ≈ 2.5, in good agreement with the linear-stability analysis performed by Yanase et al. (1993). The layer is then composed of strong longitudinal alternate absolute vortex tubes which are stretched by the flow and slightly inclined with respect to the streamwise direction. The vorticity thus generated is larger than in the nonrotating case. The Kelvin–Helmholtz vortices have been suppressed. The background velocity profile exhibits a long range of nearly constant shear whose vorticity exactly compensates the solid-body rotation vorticity. This is in agreement with the phenomenological theory proposed by Lesieur, Yanase & Métais (1991). As expected, the stretching is more efficient in the LES than in the DNS.A rotating wake has one side cyclonic and the other anticyclonic. For |Ro(i)| ≤ 1, the effect of rotation is to make the wake more two-dimensional. At moderate rotation rates (|Ro(i)| > 1), the cyclonic side is composed of Kármán vortices without longitudinal hairpin vortices. Karman vortices have disappeared from the anticyclonic side, which behaves like the mixing layer, with intense longitudinal absolute hairpin vortices. Thus, a moderate rotation has produced a dramatic symmetry breaking in the wake topology. Maximum destabilization is still observed for |Ro(i)| ≈ 2.5, as in the linear theory.The paper also analyses the effect of rotation on the energy transfers between the mean flow and the two-dimensional and three-dimensional components of the field.

scholarly journals Patterns of water in light

2019 ◽  
Vol 475 (2227) ◽  
pp. 20190110 ◽  
Author(s):  
Theodoros P. Horikis ◽  
Dimitrios J. Frantzeskakis
Keyword(s):  
Liquid Crystals ◽  
Water Waves ◽  
Soliton Solutions ◽  
Direct Numerical Simulations ◽  
Two Dimensional ◽  
Shallow Water Waves ◽  
Soliton Interactions ◽  
Non Local ◽  
Local Nonlinearity ◽  
Non Locality

The intricate patterns emerging from the interactions between soliton stripes of a two-dimensional defocusing nonlinear Schrödinger (NLS) model with a non-local nonlinearity are considered. We show that, for sufficiently strong non-locality, the model is asymptotically reduced to a Kadomtsev–Petviashvilli-II (KPII) equation, which is a common model arising in the description of shallow water waves, as such patterns of water may indeed exist in light (this non-local NLS finds applications in nonlinear optics, modelling beam propagation in media featuring thermal nonlinearities, in plasmas, and in nematic liquid crystals). This way, approximate antidark soliton solutions of the NLS model are constructed from the stable KPII line solitons. By means of direct numerical simulations, we demonstrate that non-resonant and resonant two- and three-antidark NLS stripe soliton interactions give rise to wave configurations that are found in the context of the KPII equation. Thus, our study indicates that patterns which are usually observed in water can also be found in optics.

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