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Published on: February 22, 2018
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Dynamic multiscaling in stochastically forced Burgers turbulence.
Sadhitro De1, Dhrubaditya Mitra2, Rahul Pandit1
1Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore, 560012, India.
Scientific Reports
|May 2, 2023
Summary
This study reveals an infinite number of time scales in turbulent flows using interval collapse time analysis. The probability distribution of these times is non-Gaussian with a power-law tail, offering new insights into dynamic multiscaling.
Area of Science:
- Fluid dynamics
- Statistical physics
- Nonlinear dynamics
Background:
- Turbulent flows exhibit complex dynamics and emergent scaling properties.
- The one-dimensional Burgers equation is a fundamental model for studying shock formation and turbulence.
- Understanding nonequilibrium statistically steady states is crucial in various scientific fields.
Purpose of the Study:
- To investigate dynamic multiscaling in the statistically steady state of a stochastically forced one-dimensional Burgers equation.
- To introduce and analyze the concept of interval collapse time as a measure of dynamic multiscaling.
- To determine the scaling exponents and probability distribution of interval collapse times.
Main Methods:
- Development of a theoretical framework for analytical calculation of dynamic-multiscaling exponents.
- Extensive direct numerical simulations of the stochastically forced one-dimensional Burgers equation.
- Comparison of analytical results with numerical simulation data.
Main Results:
- Identification of an infinite number of characteristic time scales in the turbulent state.
- Demonstration that the probability distribution function of interval collapse times is non-Gaussian.
- Observation of a power-law tail in the probability distribution of interval collapse times.
Conclusions:
- The turbulent state of the one-dimensional Burgers equation exhibits dynamic multiscaling with an infinite hierarchy of time scales.
- Interval collapse time is a useful concept for characterizing multiscaling in turbulent systems.
- The findings have implications for understanding shock dynamics in compressible flows and potential generalizations to higher dimensions.
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