A correspondence between the multifractal model of turbulence and the Navier-Stokes equations
| Autor: | B. Dubrulle, J. D. Gibbon |
|---|---|
| Rok vydání: | 2022 |
| Předmět: |
Science & Technology
Navier–Stokes General Science & Technology General Mathematics Fluid Dynamics (physics.flu-dyn) General Engineering Mathematics::Analysis of PDEs Navier-Stokes FOS: Physical sciences General Physics and Astronomy Physics - Fluid Dynamics FLUID Physics::Fluid Dynamics Multidisciplinary Sciences REYNOLDS PARTIAL REGULARITY TUBES SCALING LAWS intermittency ONSAGER Science & Technology - Other Topics INTENSE VORTICITY WEAK DISSIPATION multifractal |
| Zdroj: | Philosophical transactions. Series A, Mathematical, physical, and engineering sciences. 380(2218) |
| ISSN: | 1471-2962 |
| Popis: | We study a correspondence between the multifractal model of turbulence and the Navier-Stokes equations in $d$ spatial dimensions by comparing their respective dissipation length scales. In Kolmogorov's 1941 theory the key parameter $h$, which is an exponent in the Navier-Stokes invariance scaling, is fixed at $h=1/3$ but is allowed a spectrum of values in multifractal theory. Taking into account all derivatives of the Navier-Stokes equations, it is found that for this correspondence to hold the multifractal spectrum $C(h)$ must be bounded from below such that $C(h) \geq 1-3h$, which is consistent with the four-fifths law. Moreover, $h$ must also be bounded from below such that $h \geq (1-d)/3$. When $d=3$ the allowed range of $h$ is given by $h \geq -2/3$ thereby bounding $h$ away from $h=-1$. The implications of this are discussed. Comment: 9 pages, 1 figure |
| Databáze: | OpenAIRE |
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