Journal
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
Volume 111, Issue 30, Pages 10961-10965Publisher
NATL ACAD SCIENCES
DOI: 10.1073/pnas.1410791111
Keywords
fluid dynamics; energy dissipation rate
Categories
Funding
- Deutsche Forschungsgemeinschaft [1182]
- German-Israeli Foundation Grant [1072-6.14/2009]
- Direct For Computer & Info Scie & Enginr
- Office of Advanced Cyberinfrastructure (OAC) [1339773] Funding Source: National Science Foundation
- Office of Advanced Cyberinfrastructure (OAC)
- Direct For Computer & Info Scie & Enginr [1339884] Funding Source: National Science Foundation
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Turbulent flows in nature and technology possess a range of scales. The largest scales carry the memory of the physical system in which a flow is embedded. One challenge is to unravel the universal statistical properties that all turbulent flows share despite their different large-scale driving mechanisms or their particular flow geometries. In the present work, we study three turbulent flows of systematically increasing complexity. These are homogeneous and isotropic turbulence in a periodic box, turbulent shear flow between two parallel walls, and thermal convection in a closed cylindrical container. They are computed by highly resolved direct numerical simulations of the governing dynamical equations. We use these simulation data to establish two fundamental results: (i) at Reynolds numbers Re similar to 10(2) the fluctuations of the velocity derivatives pass through a transition from nearly Gaussian (or slightly sub-Gaussian) to intermittent behavior that is characteristic of fully developed high Reynolds number turbulence, and (ii) beyond the transition point, the statistics of the rate of energy dissipation in all three flows obey the same Reynolds number power laws derived for homogeneous turbulence. These results allow us to claim universality of small scales even at low Reynolds numbers. Our results shed new light on the notion of when the turbulence is fully developed at the small scales without relying on the existence of an extended inertial range.
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