Turbulence: new approaches

O M Belotserkovskii, A M Oparin, V M Chechetkin1904602223, 9781904602224, 9781423726234

The authors present the results of numerical experiments carried out to examine the problem of development of turbulence and convection. On the basis of the results, they propose a physical model of the development of turbulence. Numerical algorithms and difference schema for carrying out numerical experiments in hydrodynamics, are proposed. Original algorithms, suitable for calculation of the development of the processes of turbulence and convection in different conditions, even on astrophysical objects, are presented. The results of numerical modelling of several important phenomena having both fundamental and applied importance are described.

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Table of contents :
Contents……Page 8
1.1. Introduction……Page 10
1.2. Problem of ration ‘averaging’ in numerical examination of turbulence……Page 20
1.3. Some experimental assumptions……Page 39
1.4. General formulation of the problem……Page 44
1.5. Modelling of coherent structures in tirbulence……Page 47
1.6. Correctness of formulation of the problem……Page 53
2.1. General assumptions of construction of numerical algorithms for calculations using supercomputers……Page 57
2.2. Some numerical methods for calculatio of multidimensional nonlinear processes……Page 63
2.3. Effective quasi-monotonic hybrid scheme for gas-dynamic calculations……Page 73
2.4. Substitution of grid functions of dependent variables in finite-difference equations……Page 79
2.5. Decomposition of problems of numerical modelling, described by hyperbolic equations, on parallel computers……Page 107
2.6. Mathematical modelling of an explosion of a supernova in a parallel computer……Page 118
3.1. Calculations of coherent structures in a near wake behind a solid for limiting motion regimes……Page 133
3.2. Numerical modelling of stochastic components of turbulence (turbulent background)……Page 156
3.3. Statistical modelling of flows of free turbulence in a long-range wake……Page 173
3.4. Formation of large-scale structures in a gap between rotating cylinders (Rayleigh-Zel’dovich problem)……Page 182
3.5. Numerical simulation of the problems of development of hydrodynamic instabilities and turbulent mixing……Page 196
3.6. Numerical modelling of the processes of propagation of an impurity in the atmosphere from a large-scale source……Page 208
4.1. Turbulence……Page 222
4.2. The structure of the accretion disc……Page 226
4.3. Effect of viscosity on the morphology of the flow of matter in semi-divided binary systems. Results of three-dimensional numerical modelling……Page 244
4.4. Large-scale structure of turbulence in accretion discs……Page 258
4.5. Convective instability in astrophysics……Page 260
Conclusions……Page 275
References……Page 282
Index……Page 292