Fractal dimension crossovers in turbulent passive scalar signals

Siegfried Grossmann, Detlef Lohse

Research output: Contribution to journalArticleAcademic

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Abstract

The fractal dimension δg(1) of turbulent passive scalar signals is calculated from the fluid dynamical equation. δg(1) depends on the scale. For small Prandtl (or Schmidt) number Pr < 10-2 one gets two ranges, δg(1) = 1 for small-scale r and δg(1) = 5/3 for large r, both as expected. But for large Pr > 1 one gets a third, intermediate range in which the signal is extremely wrinkled and has δg(1) = 2. In that range the passive scalar structure function Dθ(r) has a plateau. We calculate the Pr-dependence of the crossovers. The plateau regime can be observed in a numerical solution of the fluid dynamical equation, employing a reduced wave vector set approximation introduced by us recently.
Original languageUndefined
Pages (from-to)347-352
JournalEurophysics letters
Volume27
Issue number5
DOIs
Publication statusPublished - 1994

Keywords

  • IR-50332

Cite this

Grossmann, Siegfried ; Lohse, Detlef. / Fractal dimension crossovers in turbulent passive scalar signals. In: Europhysics letters. 1994 ; Vol. 27, No. 5. pp. 347-352.
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Fractal dimension crossovers in turbulent passive scalar signals. / Grossmann, Siegfried; Lohse, Detlef.

In: Europhysics letters, Vol. 27, No. 5, 1994, p. 347-352.

Research output: Contribution to journalArticleAcademic

TY - JOUR

T1 - Fractal dimension crossovers in turbulent passive scalar signals

AU - Grossmann, Siegfried

AU - Lohse, Detlef

PY - 1994

Y1 - 1994

N2 - The fractal dimension δg(1) of turbulent passive scalar signals is calculated from the fluid dynamical equation. δg(1) depends on the scale. For small Prandtl (or Schmidt) number Pr < 10-2 one gets two ranges, δg(1) = 1 for small-scale r and δg(1) = 5/3 for large r, both as expected. But for large Pr > 1 one gets a third, intermediate range in which the signal is extremely wrinkled and has δg(1) = 2. In that range the passive scalar structure function Dθ(r) has a plateau. We calculate the Pr-dependence of the crossovers. The plateau regime can be observed in a numerical solution of the fluid dynamical equation, employing a reduced wave vector set approximation introduced by us recently.

AB - The fractal dimension δg(1) of turbulent passive scalar signals is calculated from the fluid dynamical equation. δg(1) depends on the scale. For small Prandtl (or Schmidt) number Pr < 10-2 one gets two ranges, δg(1) = 1 for small-scale r and δg(1) = 5/3 for large r, both as expected. But for large Pr > 1 one gets a third, intermediate range in which the signal is extremely wrinkled and has δg(1) = 2. In that range the passive scalar structure function Dθ(r) has a plateau. We calculate the Pr-dependence of the crossovers. The plateau regime can be observed in a numerical solution of the fluid dynamical equation, employing a reduced wave vector set approximation introduced by us recently.

KW - IR-50332

U2 - 10.1209/0295-5075/27/5/003

DO - 10.1209/0295-5075/27/5/003

M3 - Article

VL - 27

SP - 347

EP - 352

JO - Europhysics letters

JF - Europhysics letters

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