Issue |
Europhys. Lett.
Volume 50, Number 4, May II 2000
|
|
---|---|---|
Page(s) | 473 - 479 | |
Section | Electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics | |
DOI | https://doi.org/10.1209/epl/i2000-00293-9 | |
Published online | 01 September 2002 |
Anomalous scaling in a model of hydrodynamic turbulence with a small parameter
Department of Chemical Physics, The Weizmann Institute of
Science
Rehovot, 76100, Israel
Received:
15
November
1999
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
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