Approximate solution of a boundary-value problem for a model of the far momentumless turbulent wake
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A. V. Shmidt
Abstract
The flow in the far momentumless turbulent wake describes using a mathematical model based on the algebraic Rodi model of Reynolds stresses. The model is similar to the two-parameter k − ε turbulence model in the far-wake approximation with a modified empirical constants in the diffusion terms of the equations. A theoretical-group analysis of the mathematical model of the wake is performed. The similarity reduction of the model to a system of ordinary differential equations is obtained. An approximate solution and a self-similarity index of the corresponding boundary-value problem are found using an asymptotic expansion of the solution in the vicinity of a singular point.
Abstract
The flow in the far momentumless turbulent wake describes using a mathematical model based on the algebraic Rodi model of Reynolds stresses. The model is similar to the two-parameter k − ε turbulence model in the far-wake approximation with a modified empirical constants in the diffusion terms of the equations. A theoretical-group analysis of the mathematical model of the wake is performed. The similarity reduction of the model to a system of ordinary differential equations is obtained. An approximate solution and a self-similarity index of the corresponding boundary-value problem are found using an asymptotic expansion of the solution in the vicinity of a singular point.
Chapters in this book
- Frontmatter I
- Preface V
- Contents VII
- About the editors IX
- List of contributors XI
- Intermediate systems and invariants 1
- Folding in fluids 19
- Vortex models of plane turbulent flows 37
- Equations of dyon electromagnetic field 53
- Minimal action principle for gravity and electrodynamics, Einstein lambda, and Lagrange points 65
- Methods for constructing invariant conservative finite-difference schemes for hydrodynamic-type equations 83
- On exact analytical solutions of equations of Maxwell incompressible viscoelastic medium 111
- Approximate solution of a boundary-value problem for a model of the far momentumless turbulent wake 125
- Analysis of overdetermined system that describes the special class of two-dimensional motion of an ideal fluid 135
- Discrete orthogonal polynomials: anomalies of time series and boundary effects of polynomial filters 143
- Index 165
Chapters in this book
- Frontmatter I
- Preface V
- Contents VII
- About the editors IX
- List of contributors XI
- Intermediate systems and invariants 1
- Folding in fluids 19
- Vortex models of plane turbulent flows 37
- Equations of dyon electromagnetic field 53
- Minimal action principle for gravity and electrodynamics, Einstein lambda, and Lagrange points 65
- Methods for constructing invariant conservative finite-difference schemes for hydrodynamic-type equations 83
- On exact analytical solutions of equations of Maxwell incompressible viscoelastic medium 111
- Approximate solution of a boundary-value problem for a model of the far momentumless turbulent wake 125
- Analysis of overdetermined system that describes the special class of two-dimensional motion of an ideal fluid 135
- Discrete orthogonal polynomials: anomalies of time series and boundary effects of polynomial filters 143
- Index 165
