Warwick Turbulence Symposium Workshop: Non-equilibrium statistical mechanics and turbulence LMS/EPSRC short course: July 10-14, 2006 Workshop:  July 15-21, 2006

From the point of view of statistical physics, turbulence is a branch of non-equilibrium statistical mechanics dealing with states of complex systems characterized by non-zero fluxes of various conserved quantities through phase space. Though very general, this point of view turns out to be very useful. There are whole classes of non-equilibrium systems bearing no apparent resemblance to classical fluids, whose scaling properties can be studied using general phenomenology of turbulence; most notably, Kolmogorov theory developed in the context of hydrodynamic turbulence. Further, many interesting turbulent systems are simpler than Navier-Stokes systems and can in fact be studied analytically. Thus fundamental issues of the theory of turbulence (persistence of constant flux solutions, applicability limits of Kolmogorov theory, emergence of multi-fractal statistics and intermittency, the influence of dissipative structures on the statistics, etc), that are relevant for all turbulent systems, can be studied quantitatively using the powerful machinery of statistical physics. Examples of turbulent systems analysed recently from the viewpoint of non-equilibrium statistical physics, include passive scalar advection, kinematic dynamo, statistics of vorticity in two-dimensional turbulence, Burgers turbulence, stochastic rapid distortion theory, optical turbulence, cluster-cluster aggregation, directed abelian sandpile models. Mathematical methods used in this research are impressively diverse and include classical and stochastic analysis of PDEs, instanton formalism of statistical field theory, Boltzmann kinetic equation, Wilson renormalization group method.Cross-breeding between methods used in these fields is proving extremely useful. For instance, methods developed in the theory of passive advection can be used to advance further the theory of the small-scale Navier-Stokes turbulence. Another example is the Zakharov transformation, developed in the context of weak turbulence, which can be applied to derive Kolmogorov spectra in the theory of cluster-cluster aggregation.

We will hold a workshop dedicated to non-equilibrium statistical mechanics and turbulence, which will bring together specialists working in this new exciting and rapidly developing field.  Those interested to participate are invited to apply by sending us their data on the following form.

Prior to this workshop we will hold a short LMS/EPSRC sponsored course on the same subject in order to introduce main ideas and methods of statistical mechanics in turbulence to graduate students  and  to  prepare them for attending the workshop.  Applications for the course have to  be done separately as described in the following poster.

Participants

Copies of Workshop Talks