Turbulent cascade of circulations
نویسندگان
چکیده
منابع مشابه
Turbulent Cascade of Circulations
The circulation around any closed loop is a Lagrangian invariant for classical, smooth solutions of the incompressible Euler equations in any number of space dimensions. However, singular solutions relevant to turbulent flows need not preserve the classical integrals of motion. Here we generalize the Kelvin theorem on conservation of circulations to distributional solutions of Euler and give ne...
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We have emphasized the importance of developing a better understanding of the dynamical & statistical origin of the positivity of vortex-stretching rate 〈ω̄! S!ω̄!〉 > 0. For the fine-grained vorticity (! → 0), this is important in Taylor’s proposed mechanism for production of energy dissipation 〈ν|ω|2〉. For ! in the inertial-range, we have seen that the flux of energy to small-scales is proportio...
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We study material lines and passive vectors in a model of turbulent flow at infiniteReynolds number, the Kraichnan-Kazantsev ensemble of velocities that are white-noise in time and rough (Hölder continuous) in space. It is argued that the phenomenon of “spontaneous stochasticity” generalizes to material lines and that conservation of circulations generalizes to a “martingale property” of the st...
متن کاملThe Cascade of Circulations in Fluid Turbulence
Kelvin’s Theorem on conservation of circulations is an essential ingredient of G. I. Taylor’s theory of turbulent energy dissipation by the process of vortex-line stretching. In previous work, we have proposed a nonlinear mechanism for the breakdown of Kelvin’s Theorem in ideal turbulence at infinite Reynolds number. We develop here a detailed physical theory of this “cascade of circulations”. ...
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The model assumes that each step generates eddies with smaller length scales ∆x, usually ∆02. After the initial effects are forgotten, the probability distribution of vn is completely determined by the distribution W of the ‘breakdown coefficients’ vn/vn−1 (Frisch, 1995). These assumptions are known to describe well some of the statistical properties of isotropic turbulence and, in particular, ...
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ژورنال
عنوان ژورنال: Comptes Rendus Physique
سال: 2006
ISSN: 1631-0705
DOI: 10.1016/j.crhy.2006.01.008