Scaling exponents for turbulence and other random processes and their relationships with multifractal structure

Samuel I. Vainshtein, K. R. Sreenivasan, Raymond T. Pierrehumbert, Vinay Kashyap, Anurag Juneja

Research output: Contribution to journalArticle

Abstract

In the recent literature on high-Reynolds-number turbulence, several different types of scaling exponents such as multifractal exponents for velocity increments, for energy and scalar dissipation, for the square of the local vorticity, and so forth have been introduced. More recently, a new exponent called the cancellation exponent has been introduced for characterizing rapidly oscillating quantities. Not all of these exponents are independent; some of them are simply related to more familiar scaling for velocity and temperature structure functions either exactly or through plausible hypotheses familiar for turbulence. A primary purpose of this paper is to establish the interrelationships among the various exponents. In doing so, we obtain several additional relations. Much of the paper is relevant to general stochastic processes, although the discussion is heavily influenced by the turbulent context. We first examine the case of one-dimensional random processes and subsequently consider two- and three-dimensional processes. Special consideration is given to characteristic values appropriate to the geometry of turbulence, as well as the lifetimes of eddies of various scales. Finally, we discuss some properties of the tails of the probability density function to which the scaling properties of high-order structure functions are related and discuss the implications of multifractality on their structure.

Original languageEnglish (US)
Pages (from-to)1823-1835
Number of pages13
JournalPhysical Review E
Volume50
Issue number3
DOIs
StatePublished - 1994

Fingerprint

random processes
Scaling Exponent
Random process
Turbulence
turbulence
Exponent
exponents
scaling
Structure-function
Scaling
Multifractality
Cancellation
Vorticity
Probability density function
Increment
high Reynolds number
stochastic processes
Reynolds number
Stochastic Processes
Dissipation

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Condensed Matter Physics
  • Statistical and Nonlinear Physics

Cite this

Scaling exponents for turbulence and other random processes and their relationships with multifractal structure. / Vainshtein, Samuel I.; Sreenivasan, K. R.; Pierrehumbert, Raymond T.; Kashyap, Vinay; Juneja, Anurag.

In: Physical Review E, Vol. 50, No. 3, 1994, p. 1823-1835.

Research output: Contribution to journalArticle

Vainshtein, Samuel I. ; Sreenivasan, K. R. ; Pierrehumbert, Raymond T. ; Kashyap, Vinay ; Juneja, Anurag. / Scaling exponents for turbulence and other random processes and their relationships with multifractal structure. In: Physical Review E. 1994 ; Vol. 50, No. 3. pp. 1823-1835.
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