title: Small-scale universality in fluid turbulence.
abstract: 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 ∼ 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.
authors.affiliation: Department of Mechanical Engineering, Technische Universität Ilmenau, D-98684 Ilmenau, Germany;
authors.forename: Jörg
authors.initials: J
authors.lastname: Schumacher
authors.affiliation: Department of Physics, Occidental College, Los Angeles, CA 90041;
authors.forename: Janet D
authors.initials: JD
authors.lastname: Scheel
authors.affiliation: Department of Mechanical Engineering, Technische Universität Ilmenau, D-98684 Ilmenau, Germany;
authors.forename: Dmitry
authors.initials: D
authors.lastname: Krasnov
authors.affiliation: Department of Aerospace Engineering, Texas A&M University, College Station, TX 77843;
authors.forename: Diego A
authors.initials: DA
authors.lastname: Donzis
authors.affiliation: Department of Aerospace and Mechanical Engineering, Boston University, Boston, MA 02215; and.
authors.forename: Victor
authors.initials: V
authors.lastname: Yakhot
authors.affiliation: Departments of Physics and Mechanical Engineering, and the Courant Institute of Mathematical Sciences, New York University, New York, NY 10012 krs3@nyu.edu.
authors.forename: Katepalli R
authors.initials: KR
authors.lastname: Sreenivasan
keywords: energy dissipation rate; fluid dynamics