2008/04/16 by Emily S. C. Ching, H. Guo, Hongyu Guo +5
Earth and Planetary Sciences · Physics and Astronomy · #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #Oceanographic and Atmospheric Processes #nlin.CD
paper · pdf · doi:10.48550/arxiv.0804.2534
arxiv created 2008/04/16 · openalex publication_date 2008/04/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A major challenge in turbulence research is to understand from first principles the origin of anomalous scaling of the velocity fluctuations in high-Reynolds-number turbulent flows. One important idea was proposed by Kolmogorov [J. Fluid Mech. \bf 13, 82 (1962)], which attributes the anomaly to the variations of the locally averaged energy dissipation rate. Kraichnan later pointed out [J. Fluid Mech. \bf 62, 305 (1973)] that the locally averaged energy dissipation rate is not an inertial-range quantity and a proper inertial-range quantity would be the local energy transfer rate. As a result, Kraichnan's idea attributes the anomaly to the variations of the local energy transfer rate. These ideas, generally known as refined similarity hypotheses, can also be extended to study the anomalous scaling of fluctuations of an active scalar, like the temperature in turbulent convection. In this paper, we examine the validity of these refined similarity hypotheses and their extensions to an active scalar in shell models of turbulence. We find that Kraichnan's refined similarity hypothesis and its extension are valid.