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Nonuniversal power-law spectra in turbulent systems
V Bratanov1, F Jenko, D R Hatch
1Max-Planck-Institut für Plasmaphysik, EURATOM Association, 85748 Garching, Germany.
Physical Review Letters
|September 3, 2013
Summary
Turbulence often shows universal power-law spectra. This study models systems without universal ranges, finding nonuniversal power-law exponents in modified Kuramoto-Sivashinsky turbulence.
Area of Science:
- Fluid dynamics
- Nonlinear dynamics
- Statistical physics
Background:
- Turbulence typically exhibits universal power-law spectra in inertial ranges.
- However, many turbulent systems lack a clear inertial range, yet still display power-law spectra.
- Understanding these non-universal spectral behaviors is crucial for a complete theory of turbulence.
Purpose of the Study:
- To investigate the emergence of power-law spectra in turbulent systems lacking universal inertial ranges.
- To model such systems using a modified Kuramoto-Sivashinsky equation.
- To determine the characteristics of these power-law spectra and their exponents.
Main Methods:
- Utilized a modified Kuramoto-Sivashinsky equation as a simplified model for turbulence.
- Employed semianalytical techniques to analyze the model's behavior.
- Conducted numerical simulations to complement the analytical findings.
Main Results:
- Identified power-law spectra in the studied spectral range.
- Found that the exponents of these power laws are nonuniversal.
- Observed these nonuniversal power laws in regions where the ratio of nonlinear to linear time scales is approximately scale-independent.
Conclusions:
- The modified Kuramoto-Sivashinsky equation provides a viable model for turbulent systems with nonuniversal power-law spectra.
- Nonuniversal exponents arise in specific scale ranges characterized by a scale-independent ratio of time scales.
- This work contributes to understanding spectral properties of turbulence beyond the standard inertial range framework.
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