Reference+Material

Here's a page to share important papers, review articles, relevant news, etc.
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__**Anisotropic Turbulence**__
Paper on experiment in axially anisotropic turbulence K. Chang, G. Bewley, E. Bodenschatz: [] 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:
 * Upscale energy transfer in thick turbulent fluid layers**, H. Xia, D. Byrne , G. Falkovich and M. Shats (2011) [|//Nature Physics//: Advanced Online Publication][|[ PDF]]

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**, <span style="font-family: 'Gill Sans',Helvetica,Arial,sans-serif; font-size: 14px; line-height: normal;">//Physical Review Letters//, 101, <span style="font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 12px; line-height: 18px;">254102 (2008) [|Link]. <span style="font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 12px; line-height: 18px;">Th. Walter, W. Pesch, E. Bodenschatz, **Dislocation Dynamics in Rayleigh-Bénard Convection**, Chaos 14, 933 (2004) [|link]

__<span style="font-family: Arial,Helvetica,sans-serif;">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, <span style="font-family: Arial,Helvetica,sans-serif; font-size: 14px; line-height: 21px;">[|PRA 81: 033611, 2010] <span style="font-family: Arial,Helvetica,sans-serif; font-size: 14px; line-height: 21px;">[|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, <span style="font-family: Arial,Helvetica,sans-serif; font-size: 14px; line-height: 21px;">[|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 <span style="font-family: Arial,Helvetica,sans-serif; font-size: 14px; line-height: 21px;">[|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)
 * <span style="font-family: Helvetica,Arial,sans-serif;">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__
> in //Scientific Computing and Applications// edited by P. Minev, Y.S. Wong, and Y. Lin, volume 7 of //Advances in Computation: Theory and Practice//, Nova Science Publishers, 171-178 (2001).
 * R.H. Kraichnan, in //Theoretical Approaches to Turbulence,// edited by D. L. Dwoyer, M. Y. Hussaini and, R. G. Voigt, Springer (1985).
 * V. Yakhot and S. A. Orszag, J. Sci. Comput. **1,** 3-51 (1986).
 * G. Eyink, [|Phys. Rev. E 48, 1823–1838 (1993)]
 * Siegfried Grossmann, Detlef Lohse, and Achim Reeh, [|Phys. Rev. Lett. 77, 5369 (1996)].
 * P. Holmes, J.L. Lumley and G. Berkooz, ``Turbulence, Coherent Structures, Dynamical Systems, and Symmetry'', Cambridge University Press (1996).
 * J.C. Bowman, B.A. Shadwick, and P.J. Morrison, [|Spectral reduction: a statistical description of turbulence]//Phys. Rev. Lett.//**83**, 5491-5494 (1999).
 * J.C. Bowman, B.A. Shadwick, and P.J. Morrison, [|Numerical Challenges for Turbulence Computation: Statistical Equipartition and the Method of Spectral Reduction]
 * Tutorial on Statistical Closures: [|Realizable Markovian Closures,]//Stochastic Modeling of Geophysical Flows Workshop//, NCAR (March, 2003). See also J. C. Bowman, J. A. Krommes, and M. Ottaviani, [|Phys. Fluids B 5, 3558 (1993)] and J. C. Bowman and J. A. Krommes, [|Phys. Plasmas 4, 3895-3909 (1997).], and J. A. Krommes, "Fundamental statistical theories of plasma turbulence in magnetic fields," [|Phys. Reports, Vol. 360, 1-351 (2002)].

__Visualization Software__

 * [|Asymptote: 2D & 3D TeX-aware vector graphics language] (embeds 3D vector PRC graphics within PDF files).

__**N****umerical Methods**__

 * [|Implicitly dealiased FFT-based convolutions]
 * [|Exactly conservative integrators]
 * [|Lagrangian advection:] preserves higher-order Casimir invariants by enforcing finite parcel rearrangement
 * [|Exponential integrators]
 * Wavelet methods
 * Adaptive methods
 * Decomposition into coherent and incoherent parts: [|coherent vortex simulation] (CVS)
 * The "[|tyger phenomenon]" that may lead to a way to automatic capture shocks in spectral 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