704 Mathematics and Computations for Multiscale Structures of Turbulent and Other Complex Flows

Yuli D Chashechkin, Institute for Problems in Mechanics of the Russian Academy of Sciences
Chaoqun Liu, University of Texas at Arlington
Historically, hydrodynamics is one of the main users of mathematical methods and results and, in turn, an important source of new problems for mathematical research. The constructive ideas of D’Alembert, Euler, Fourier, Navier, Stokes and Fick formed the basis for the mathematical calculation of flows, for classification of empirical models, and had a decisive impact on the development of the experimental techniques. In the second half of the nineteenth century, new models were constructed, based on theories of linear or nonlinear waves, vortices and turbulence. Since the beginning of the twentieth century, the ideas of the boundary layer have spread. The development of new environmental and industrial technologies stimulated the development of turbulence models (including the Reynolds-averaged Navier-Stokes equations). However, the lack of a proof of the 3D Navier-Stokes equations solvability restrains the development of the theory of flows and the technique of comparison with experiment.
Modern optical instruments revealed such structures in flow patterns, as waves, vortices, jets, wakes, separating high-gradient interfaces and fine filaments. Dynamic multiscale structures are observing in flows of all types of fluids, gases and plasma in the entire range of spatial and temporal scales available – from microscopic to galactic. The study of multiscale structures helps to understand mechanisms of basic physical states of natural systems formation (in particular, stellar and planetary atmospheres, hydrosphere and geosphere) and identification of basic processes causing their changes. Mathematics of flow structures helps to estimate their influence on the transport of energy and matter, to improve the prediction of the evolution of separate processes and natural systems in general, to calculate the interaction of liquids and solids, to develop methods of processes control in complex systems. 
The goal of this mini-symposium is to discuss different analytical and numerical methods for the coordinated calculation of the dynamics and multiscale structure of heterogeneous fluid flows, to compare the principles of structural components identification and classification of structural forms, to estimate methods of comparisons the results of different models with each other, with observations of natural systems and data of laboratory modelling.