Anomalous Scaling in a Model of Hydrodynamic Turbulence with a Small Parameter

Details Anomalous Scaling in a Model of Hydrodynamic Turbulence with a Small Parameter Anomalous Scaling in a Model of Hydrodynamic Turbulence with a Small Parameter

1999-03-23

arxiv.org/abs/chao-dyn/9903030v1

Nonlinear Sciences

Chaotic Dynamics

REVTeX, 4 pages, 5 eps figures included, submitted to PRL. Online (HTML) and PS versions of this and related papers available

Scientific paper

10.1209/epl/i2000-00293-9

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 small parameter. The small parameter $\epsilon$ represents the ratio between deterministic and random components in the coupling between $N$ identical copies of the turbulent field. We show that in the limit $N\to \infty$ anomalous scaling sets in proportional to $\epsilon^4$. Moreover we give strong evidences that the birth of anomalous scaling appears at a finite critical $\epsilon$, being $\epsilon_c\approx 0.6$.

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