Folding in fluids
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E. A. Kuznetsov
Abstract
The formation of the coherent vortical structures in the form of thin pancakes for three-dimensional flows is studied at the high Reynolds regime when, in the leading order, the development of such structures can be described within the Euler equations for ideal incompressible fluids. Numerically and analytically on the base of the vortex line representation, we show that compression of such structures and, respectively, increase of their amplitudes are possible due to the compressibility of the vorticity in the 3D case. It is demonstrated that this growth has an exponential behavior and can be considered as folding (analog of breaking) for the divergence-free fields of vorticity. At high amplitudes, this process in 3D has a self-similar behavior connected the maximal vorticity and the pancake width by the relation of the universal type [1].
Abstract
The formation of the coherent vortical structures in the form of thin pancakes for three-dimensional flows is studied at the high Reynolds regime when, in the leading order, the development of such structures can be described within the Euler equations for ideal incompressible fluids. Numerically and analytically on the base of the vortex line representation, we show that compression of such structures and, respectively, increase of their amplitudes are possible due to the compressibility of the vorticity in the 3D case. It is demonstrated that this growth has an exponential behavior and can be considered as folding (analog of breaking) for the divergence-free fields of vorticity. At high amplitudes, this process in 3D has a self-similar behavior connected the maximal vorticity and the pancake width by the relation of the universal type [1].
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
