Dissipative Structures and Weak Turbulence

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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. The final chapter deals with building a bridge between chaos as studied in weakly confined systems and more advanced turbulence in the most conventional sense. Rotorcraft Aeromechanics. Wayne Johnson.

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