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Warwick Turbulence Symposium Workshop on: Universal features in turbulence: from quantum to cosmological scales Co-sponsored by EPSRC and ESF (COSLAB,QUDEDIS and STOCHDYN programmes)         Organisers: STOCHDYN: Peter McClintock Warwick: Sergey Nazarenko COSLAB:  Grisha Volovik QUDEDIS: Martin Wilkens                           December 5-10, 2005.

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The main goal of the workshop is to establish collaboration between different communities working on inter-disciplinary problems of nonlinear dynamics of
macroscopic systems far from equilibrium. The particular topic of the workshop is turbulence in different systems.  There is a new direction in the study of the phenomenon of turbulence -- the quantum turbulence, i.e. turbulence in such complex quantum systems as superfluids and Bose and Fermi condensates of ultracold atoms.  The quantum turbulence bears the essential features of classical turbulence, since it also represents the chaotic dynamics of vortex lines. The advantage of the quantum system is that vortices there are well  isolated from each other and this is more simple for analytic and numerical investigations. That is why its study can help to shed light on the long-standing puzzles of the phenomenon of turbulence in general.

On the other hand the macroscopic quantum systems have many common properties with quantumvacuum of our Universe, which allows us to simulate the Universe and its dynamics in laboratory.


Essential part of the workshop is concentrated on new features of quantum turbulence compared to the classical one. The onset of turbulence, the Kolmogorov cascade in developed turbulence, and decay of turbulence, all these are modified in the quantum regime especially at low temperature when the dissipation practically vanishes.  Such regime can never occur in conventional classical liquids. Some of the most surprising new features are : the observation of the sharp phase transition between the laminar and turbulent  states which is governed by the velocity-independent internal parameter of a quantum liquid; the non-Kolmogorov energy cascade
in developed quantum turbulence; weak turbulence on a vortex filaments (the so called Kelvin wave turbulence) which is an extension of the weak turbulence of the
capillary waves to the one-dimensional case; etc.

On the other hand, the instabilities in quantum systems which lead to formation of quantized vortices and then to quantum turbulence, share many common features
with the instabilities discussed in quantum vacuum of relativistic quantum fields. In particular, the instability of the surface of the rotating Bose condensate or of the interface between two sliding superfluid liquids have the same origin  as the instability of the quantum vacuum behind the black-hole event horizon. The reason for that is that the ground state of quantum systems serves as an analogue of the vacuum in relativisic systems. This opens the possibility to simulate experimentally in superfluids and in cold gases the properties of the quantum vacuum in the presence of black-hole and white-hole horizons and even the physical singularity inside the
black hole. This is one of many points for collaboration of condensed-matter community with cosmological and high energy communities.

Among the other common topics -- the properties shared by quantized vortices and cosmic strings. For example, the reconnection of vortices and formation of a kink (cusp) play an important role in the development of quantum turbulence at low temperature. These cusp-like singularities give rise to the burst of Kelvin waves and/or fermionic quasiparticles in Fermi superfluids and condensates. These singularities are similar to that on cosmic strings, where they give rise to the burst of gravitational waves and other radiation from cosmic strings. There are other aspects common to condensed-matter and cosmology in relation to turbulence, for example, the "chaotic turbulence" of space near a big crunch singularity.


All these phenomena have many common features also with phenomena in classical hydrodynamics, that is why the collaboration with this community is highly
welcome. The expertise obtained by study of turbulence in classical liquids is very important for quantum turbulence.  The turbulence in classical liquids is thought to be characterized by the dynamics of the vortex tubes, whose radii are of order of the dissipative Kolmogorov scale. In some  regime, the superfluid turbulence is similar to that in classical liquids with modified dissipation. Thus the quantum liquid serves as a physically motivated example of the liquid with the non-canonical
dissipation, which requires the general analysis of different models of dissipation and forcing. It also allows to study the general problem of intermittency -- emergence of rare but large events (large vortex loops in case of quantum turbulence).  All this can give a new impulse for our understanding of the main concepts of the
phenomen of turbulence in general.


Recent progress in the theory of stochastical systems revealed that many of the non-equilibrium statistical systems are better described by the phase-space energy fluxes rather than thermodynamic temperature and chemical potential. As a result, the has been a surge of interest of the stochastic dynamics specialists in turbulence, which is the most classical example of non-equilibrium state determined by a flux, - the Kolmogorov energy cascade through scales. There exist turbulent systems of special interest which allow complete theoretical treatement. One of them,  passive scalar advected by a stochastic velocity field, was recently solved and in our conference we are going to have a review talk on this subject. This will help application of methods developed in this subject to be applied to other important systems of stochastic dynamics and turbulence (e.g. zero modes, instanton formalism). Another example of turbulent stochastic dynamics which allows theoretical treatment is a system of weakly nonlinear random dispersive waves, e.g. waves on sea after a fresh storm, Alfven waves in interstellar medium or even cosmological waves during the inflation reheating. We are going to have a section devoted to these systems and review various aspects of this fastly developing area.




Figure: "turbulent"  microwave background field due to cosmic strings (borrowed from http://www.damtp.cam.ac.uk/user/gr/public/cs_home.html):