Steep Cliffs and Saturated Exponents in Three-Dimensional Scalar Turbulence

Kartik P. Iyer, Jörg Schumacher, Katepalli Sreenivasan, P. K. Yeung

Research output: Contribution to journalArticle

Abstract

The intermittency of a passive scalar advected by three-dimensional Navier-Stokes turbulence at a Taylor-scale Reynolds number of 650 is studied using direct numerical simulations on a 40963 grid; the Schmidt number is unity. By measuring scalar increment moments of high orders, while ensuring statistical convergence, we provide unambiguous evidence that the scaling exponents saturate to 1.2 for moment orders beyond about 12, indicating that scalar intermittency is dominated by the most singular shocklike cliffs in the scalar field. We show that the fractal dimension of the spatial support of steep cliffs is about 1.8, whose sum with the saturation exponent value of 1.2 adds up to the space dimension of 3, thus demonstrating a deep connection between the geometry and statistics in turbulent scalar mixing. The anomaly for the fourth and sixth order moments is comparable to that in the Kraichnan model for the roughness exponent of 4/3.

Original languageEnglish (US)
Article number264501
JournalPhysical Review Letters
Volume121
Issue number26
DOIs
StatePublished - Dec 28 2018

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cliffs
turbulence
exponents
scalars
intermittency
moments
Schmidt number
direct numerical simulation
unity
fractals
Reynolds number
roughness
grids
statistics
anomalies
saturation
scaling
geometry

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

Steep Cliffs and Saturated Exponents in Three-Dimensional Scalar Turbulence. / Iyer, Kartik P.; Schumacher, Jörg; Sreenivasan, Katepalli; Yeung, P. K.

In: Physical Review Letters, Vol. 121, No. 26, 264501, 28.12.2018.

Research output: Contribution to journalArticle

Iyer, Kartik P. ; Schumacher, Jörg ; Sreenivasan, Katepalli ; Yeung, P. K. / Steep Cliffs and Saturated Exponents in Three-Dimensional Scalar Turbulence. In: Physical Review Letters. 2018 ; Vol. 121, No. 26.
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