Here's a page to share important papers, review articles, relevant news, etc.

Anisotropic Turbulence

Paper on experiment in axially anisotropic turbulence K. Chang, G. Bewley, E. Bodenschatz:
Upscale energy transfer in thick turbulent fluid layers, H. Xia , D. Byrne , G. Falkovich and M. Shats (2011) //Nature Physics//: Advanced Online Publication [ PDF]
Looking for new problems to solve? Consider the climate, J. B. Marston: Physics Trends 4, 20 (2011)
Very mild nonhomogeneity (absence of a mean shear) but substantial anisotropy:
how small scales perceive it. D. Tordella and M.Iovieno Small scale anisotropy in shearless mixing, 2011, in revision for PRL.
how large scale perceive it: D.Tordella, PR Bailey, M.Iovieno Sufficient condition for Gaussian departure in turbulence 2008 PRE
passiva scalar and velocity spectra inside the interaction layer between two isotropic turbulences, see pages 6-8 in the work in progress file:

Quantum Turbulence

New work by R. Kerr:
This is supporting material on Vortex stretching as a mechanism for quantum kinetic energy decay for my PRL that has just been conditionally accepted.
I plan on an informal discussion about the latest work at 2PM, Thursday, 10 February. Location hasn't been set and will be in an office if nothing else is available. My presentation next week will start with the historical background on quantum turbulence and how this has led us to viewing the Gross-Piteavskii equation (as will be reviewed by Falkovich) as a better simplification of the underlying equation for quantum turbulence in superfluids than traditional vortex based models.

preprint on vortex motion in superfluids

Laboratory Astrophysics

Newtonian hypersonic jets in partial similitude with YSO optical jets: Axial high density regions are present even in the absence of the magnetic filed.
Under-expanded jets: scaling of the barrel and normal shocks with jet/ambient density ratio and Mach number

Experiments in Turbulence

Please post here your experimental talks and papers.

The Göttingen Turbulence Facility

Defect (Dislocation) Turbulence

A selection on papers on defect turbulence in inclined layer convection and the Complex Ginzburg Landau Equation. Defect turbulence seems to share properties of quantum turbulence. Especially the defect velocity PDF has the same power law as vortex reconnections (see Fig 9 . Chaos, 13:55, March 2003).

Karen E. Daniels, Brendan B. Plapp, and Eberhard Bodenschatz. Pattern formation in inclined layer convection. Physical Review Letters, 84:5320-5323, June 5 2000. [Link]
Karen E. Daniels and Eberhard Bodenschatz. Defect turbulence in inclined layer convection. Physical Review Letters, 88:034501, January 7 2002. [Link]
Karen E. Daniels and Eberhard Bodenschatz. Statistics of defect motion in spatiotemporal chaos in inclined layer convection. Chaos, 13:55, March 2003. [Link]
Cristian Huepe, Hermann Riecke, Karen E. Daniels, and Eberhard Bodenschatz. Statistics of defect trajectories in spatio-temporal chaos in inclined layer convection and the complex Ginzburg-Landau equation. Chaos, 14:864-874, Sep 2004. [Link]
Karen E. Daniels, Christian Beck, and Eberhard Bodenschatz. Defect turbulence and generalized statistical mechanics. Physica D, 193:208, 2004. [Link]

Dislocation Dynamics:

Eberhard Bodenschatz, Wener Pesch and L. Kramer. Structure and Dynamics of Defects in Anisotropic Pattern Forming Systems Physica D, 32:135:145, April 22, 1988 [Link]
J. H. McCoy, W. Brunner, W. Pesch, E. Bodenschatz, Self-organization of topological defects due to applied constraints, Physical Review Letters, 101, 254102 (2008) Link.
Th. Walter, W. Pesch, E. Bodenschatz, Dislocation Dynamics in Rayleigh-Bénard Convection, Chaos 14 , 933 (2004)link

Collective behaviour of perturbative waves in shear flows

In order to understand whether, and to what extent, spectral representation can effectively highlight the nonlinear interaction among different scales, it is necessary to consider the state that precedes the onset of instabilities and turbulence in flows . In this condition, a system is still stable, but is however subject to a swarming of arbitrary three-dimensional small perturbations. These can arrive any instant, and then a transient evolution which is ruled out by the initial value problem associated to the Navier-Stokes linearized formulation. The set of all possible 3D small perturbations constitutes a system of multiple spatial and temporal scales which are subject to all the processes included in the perturbative Navier-Stokes equations: linearized convective transport, linearized vortical stretching and tilting, and the molecular diffusion. Leaving aside nonlinear interaction among the different scales, these features are tantamount to the features of the turbulent state.
If it were possible to observe such a system in a temporal window and obtain the instantaneous 3D wave number spectra, it would be possible, among others, to determine the exponent of the inertial range of the arbitrary perturbation evolution, and to compare it with the exponent of the corresponding developed turbulent state (notoriously equal to - 5/3). Two possible situations can therefore appear. A -The exponent difference is large, and as such, is a quantitative measure of the nonlinear interaction in spectral terms. B - The difference is small. This would be even more interesting, because it would indicate a higher level of universality on the value of the exponent of the inertial range, not necessarily associated to the nonlinear interaction.

Matter-wave (quantum) turbulence: Beyond kinetic scaling

by Christian Scheppach, Jürgen Berges, and Thomas Gasenzer,
PRA 81: 033611, 2010
arXiv:0912.4183 [cond-mat.quant.gas]
Turbulent scaling phenomena are studied in an ultracold Bose gas away from thermal equilibrium. Fixed points of the dynamical evolution are characterized in terms of universal scaling exponents of correlation functions. The scaling behavior is determined analytically in the framework of quantum field theory, using a nonperturbative approximation of the two-particle irreducible effective action. While perturbative Kolmogorov scaling is recovered at higher energies, scaling solutions with anomalously large exponents arise in the infrared regime of the turbulence spectrum. The extraordinary enhancement in the momentum dependence of long-range correlations could be experimentally accessible in dilute ultracold atomic gases. Such experiments have the potential to provide insight into dynamical phenomena directly relevant also in other present-day focus areas like heavy-ion collisions and early-universe cosmology.

Quantum turbulence in an ultracold Bose gas

by Boris Nowak, Denes Sexty, and Thomas Gasenzer,
arXiv:1012.4437 [cond-mat.quant.gas]
Quantum turbulence in a dilute degenerate Bose gas is analysed in two and three spatial dimensions. Special focus is set on the infrared regime of large-scale vortical flow in which universal power-law distributions are found. These power laws, previously predicted within an analytic quantum-field-theoretic approach are confirmed by means of simulations using the classical field equation. Their relation to the well-known Kolmogorov 5/3 law is discussed. In this way a connection is established between nonthermal fixed points of quantum-field-theoretic equations and the nature of vortex dynamics in a superfluid. The predicted dynamics should be accessible with modern experimental technology and has the potential to shed light on fundamental aspects of turbulence.

Time scales of turbulence

by Dhrubaditya Mitra, Rahul Pandit, Prasad Perlekar and Samriddhi Sankar Ray
Persistence in two dimensional turbulence

We are interested in the question of characteristic time scales of turbulence.

One aspect of this question is addressed by studying time-dependent structure functions, which are generalisations of
the standard Kolmogorov like structure functions. It has been argued that time-dependent structure functions show dynamic multiscaling,
which means :
(a) time-dependent structures functions corresponding to different length scales cannot be collapsed by a single
dynamic exponent -- lack of simple dynamical scaling.
(b) But characteristic time scale, e.g., the integral time scale will show scaling. However the dynamic scaling exponents
will depend on exactly how the characteristic time scales are defined.
(c) Such dynamic exponents can be related to the equal-time scaling exponents (the standard zeta_p s )
by bridge relations. Such bridge relations can be extracted from the multifractal model.

Useful references:
  • V.S. L’vov, E. Podivilov, and I. Procaccia, Phys. Rev. E 55 7030 (1997)
  • L. Biferale, G. Bofetta, A. Celani, and F. Toschi, Physica D 127 187 (1999).
  • D. Mitra and R. Pandit Phys. Rev. Lett. 93, 024501 (2004)
  • D. Mitra and R. Pandit Phys. Rev. Lett. 95, 144501 (2005)
  • S.S. Ray, D. Mitra and R. Pandit New J. Phys. 10 (2008) 033003

The question about time scales can also posed in a different manner by asking, e.g., how long does a vortex live ?
Such questions can be mathematically formulated as a first passage problem, which forms a bridge between
turbulence and the field of persistence in nonequilibrium statistical mechanics.
The clue here is to use topological invariants (e.g., the Okubo-Weiss parameter in two dimensions) to define
a vortex. From direct numerical simulations of two dimensional turbulence we find the probability distrubution
of lifetime of vortices. Such a PDF shows power law tail with possibly universal exponent -- the persistence exponent.

Useful reference :
  • P. Perlekar, S.S. Ray, D. Mitra and R. Pandit Phys. Rev. Lett. 106, 054501 (2011)

Reduced Models

Visualization Software

Numerical Methods

Historical papers

1933 Prandtl Turbulent flow in smooth and rough pipes
1938 Motzfeld Spectrum of channel flow
1938 Prandtl Turbulence behind grid, decay, spectrum, channel flow
1927 Prandtl Wilbur Wright Memorial Lecture
2010 Prandtl and the Goettingen School, E. Bodenschatz and Michael Eckert, preprint.

2011 Kolmogorov and the Russian School, G. Falkovich, preprint