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Varieties of dynamic multiscaling in fluid turbulence
Dhrubaditya Mitra1, Rahul Pandit
1Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560012, India.
Physical Review Letters
|August 25, 2004
Summary
Different methods for extracting time scales from fluid turbulence data yield distinct dynamic-multiscaling exponents. These exponents connect to equal-time exponents via derived bridge relations, confirmed by shell model simulations.
Area of Science:
- Physics
- Fluid Dynamics
- Turbulence Theory
Background:
- Multiscaling is a key feature of developed fluid turbulence.
- Structure functions are crucial for analyzing turbulent systems.
- Extracting dynamic exponents from time-dependent data presents challenges.
Purpose of the Study:
- To investigate how different methods of time scale extraction affect dynamic-multiscaling exponents in fluid turbulence.
- To derive and validate bridge relations connecting time-dependent and equal-time multiscaling exponents.
- To generalize findings to other multiscaling systems.
Main Methods:
- Analysis of time-dependent velocity structure functions.
- Derivation of bridge relations between different multiscaling exponents.
- Numerical simulations using the Gledzer-Ohkitani-Yamada (GOY) shell model for fluid turbulence.
Main Results:
- Different time scale extraction methods lead to distinct dynamic-multiscaling exponents.
- The derived bridge relations accurately connect time-dependent and equal-time multiscaling exponents.
- Numerical simulations confirm the theoretical predictions for the GOY shell model.
Conclusions:
- The choice of time scale extraction method is critical for determining dynamic-multiscaling exponents in turbulence.
- The established bridge relations provide a robust framework for relating different multiscaling descriptions.
- The findings are applicable to a broad range of systems exhibiting multiscaling behavior.
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