Physica A 338 (2004) 194–200 www.elsevier.com/locate/physa Universality of anisotropic turbulence L. Biferale a; b; ∗ , E. Calzavarini c , A.S. Lanotte b; e , F. Toschi b; d , R. Tripiccione c a Via della Ricerca Scientica 1, INFM, Unit a di Tor Vergata, Universit a di Tor Vergata, I-00133 Roma, Italy b Via della Ricerca Scientica 1, INFM, Unit a di Tor Vergata, I-00133 Roma, Italy c Universit a di Ferrara and INFN, Via Paradiso 12, I-43100 Ferrara, Italy d Istituto per le Applicazioni del Calcolo, CNR, Viale del Policlinico 137, I-00161 Roma, Italy e CNR, ISAC-Sezione di Lecce, Str. Prov. Lecce-Monteroni Km 1.200, I-73100 Lecce, Italy Abstract We review some ideas about the physics of small-scale turbulent statistics, focusing on the scaling behavior of anisotropic uctuations. We present results from direct numerical simula- tions of three-dimensional homogeneous, anisotropically forced, turbulent systems: the Rayleigh– B enard system, the random-Kolmogorov-ow, and a third ow with constant anisotropic energy spectrum at low wave numbers. A comparison of the anisotropic scaling properties displays good similarity among these very dierent ows. Our ndings support the conclusion that scaling ex- ponents of anisotropic uctuations are universal, i.e., independent of the forcing mechanism sustaining turbulence. c 2004 Elsevier B.V. All rights reserved. PACS: 47.27.-i; 47.27.Gs Keywords: Turbulent ows; Homogeneous turbulence; Convection In recent years theoretical, numerical and experimental work has been done to study the statistics of small scales in turbulent ows [1]. The understanding of universal- ity has been the central matter of investigation in the scientic community. By uni- versality, we mean to which extent small-scale turbulent uctuations are statistically independent of the large-scale set-up used to inject energy in the ow. Actually, ro- bustness of small-scale physics cannot be really exact; for instance, dierent forcings * Corresponding author. Via della Ricerca Scientica 1, INFM, Unit a di Tor Vergata, Universit a di Tor Vergata, Roma 00133, Italy. Fax: +39-06-2023507. E-mail address: biferale@roma2.infn.it (L. Biferale). 0378-4371/$ - see front matter c 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.physa.2004.02.041