Preliminaries -- Contents -- 1. Fundamental aspects of the direct numerical modelling of free turbulence and hydrodynamic instabilities -- 1.1. Introduction -- 1.2. Problem of ration 'averaging' in numerical examination of turbulence -- 1.3. Some experimental assumptions -- 1.4. General formulation of the problem -- 1.5. Modelling of coherent structures in tirbulence -- 1.6. Correctness of formulation of the problem -- 2. Computing problems and methods of examining nonlinear multidimensional problems -- 2.1. General assumptions of construction of numerical algorithms for calculations using supercomputers -- 2.2. Some numerical methods for calculatio of multidimensional nonlinear processes -- 2.3. Effective quasi-monotonic hybrid scheme for gas-dynamic calculations -- 2.4. Substitution of grid functions of dependent variables in finite-difference equations -- 2.5. Decomposition of problems of numerical modelling, described by hyperbolic equations, on parallel computers -- 2.6. Mathematical modelling of an explosion of a supernova in a parallel computer -- 3. Selected results -- 3.1. Calculations of coherent structures in a near wake behind a solid for limiting motion regimes -- 3.2. Numerical modelling of stochastic components of turbulence (turbulent background) -- 3.3. Statistical modelling of flows of free turbulence in a long-range wake -- 3.4. Formation of large-scale structures in a gap between rotating cylinders (Rayleigh-Zel'dovich problem) -- 3.5. Numerical simulation of the problems of development of hydrodynamic instabilities and turbulent mixing -- 3.6. Numerical modelling of the processes of propagation of an impurity in the atmosphere from a large-scale source -- 4. Astrophysical turbulence, convection and instabilities -- 4.1. Turbulence -- 4.2. The structure of the accretion disc.

4.3. Effect of viscosity on the morphology of the flow of matter in semi-divided binary systems. Results of three-dimensional numerical modelling -- 4.4. Large-scale structure of turbulence in accretion discs -- 4.5. Convective instability in astrophysics -- Conclusions -- References -- Index.