Extended Self-Similarity in Turbulent Systems: an Analytically Soluble Example

Details Extended Self-Similarity in Turbulent Systems: an Analytically Soluble Example Extended Self-Similarity in Turbulent Systems: an Analytically Soluble Example

1996-01-03

arxiv.org/abs/chao-dyn/9601002v1

PRL v.76 1828 (1996)

Nonlinear Sciences

Chaotic Dynamics

Phys. Rev. Lett., submitted, RevTeX, 4 pages, two figures by request from Daniel Segel: daniel@dvir.weizmann.ac.il

Scientific paper

10.1103/PhysRevLett.76.1828

In turbulent flows the $n$'th order structure functions $S_n(R)$ scale like $R^{\zeta_n}$ when $R$ is in the "inertial range". Extended Self-Similarity refers to the substantial increase in the range of power law behaviour of $S_n(R)$ when they are plotted as a function of $S_2(R)$ or $S_3(R)$. In this Letter we demonstrate this phenomenon analytically in the context of the ``multiscaling" turbulent advection of a passive scalar. This model gives rise to a series of differential equations for the structure functions $S_n(R)$ which can be solved and shown to exhibit extended self similarity. The phenomenon is understood by comparing the equations for $S_n(R)$ to those for $S_n(S_2)$.

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