Anomalous scaling in a model of hydrodynamic turbulence with a small parameter
Department of Chemical Physics, The Weizmann Institute of
Rehovot, 76100, Israel
Accepted: 20 March 2000
The major difficulty in developing theories for anomalous scaling in hydrodynamic turbulence is the lack of a small parameter. In this letter we introduce a shell model of turbulence that exhibits anomalous scaling with a tunable parameter ϵ, , representing the ratio between deterministic and random components in the coupling between N identical copies of the turbulent field. Our numerical experiments give strong evidence that in the limit anomalous scaling sets in proportional to . This result shows consistency with the nonperturbative closure proposed by the authors in Phys. Fluids, 12 (2000) 803. In this procedure closed equations of motion for the low-order correlation and response functions are obtained, keeping terms proportional to and , discarding terms of orders and higher. Moreover we give strong evidences that the birth of anomalous scaling appears at a finite critical ϵ, being .
PACS: 47.27.Gs – Isotropic turbulence; homogeneous turbulence / 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion / 47.27.Jv – High-Reynolds-number turbulence
© EDP Sciences, 2000