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Inverse energy cascade in three-dimensional isotropic turbulence
Luca Biferale1, Stefano Musacchio, Federico Toschi
1Department of Physics & INFN, Università Tor Vergata, Via della Ricerca Scientifica 1, 00133 Rome, Italy.
Physical Review Letters
|June 12, 2012
Summary
All three-dimensional turbulent flows exhibit reverse energy transfer, moving energy from small to large scales. This inverse cascade, driven by broken mirror symmetry, highlights the universal role of helicity in fluid dynamics.
Area of Science:
- Fluid Dynamics
- Turbulence Theory
- Statistical Mechanics
Background:
- Turbulent flows are typically characterized by energy transfer from large to small scales.
- An inverse energy cascade (energy transfer from small to large scales) has been previously observed only in specific conditions like rotating flows or quasi-two-dimensional geometries.
- Helicity, a measure of the alignment of vorticity and velocity, plays a role in energy transfer, particularly in 2D systems.
Purpose of the Study:
- To investigate the statistical properties of three-dimensional (3D) turbulent flows.
- To determine if an inverse energy cascade occurs in general 3D flows beyond previously known conditions.
- To elucidate the role of helicity in the energy transfer mechanisms within turbulent systems.
Main Methods:
- Development of a novel numerical method for investigating Navier-Stokes equations.
- Application of Galerkin decimation of helical Fourier modes for numerical simulations.
- Analysis of energy transfer and helicity distribution across different scales.
Main Results:
- Demonstration that all 3D turbulent flows possess nonlinear evolution leading to a reverse energy transfer (small to large scales).
- Confirmation that energy flux reversal occurs universally when mirror symmetry is broken.
- Observation of a well-defined sign distribution of helicity across all wave numbers.
Conclusions:
- The inverse energy cascade is a general phenomenon in 3D turbulent flows, not limited to specific geometries or rotation.
- Broken mirror symmetry is a key condition for the inverse energy cascade in 3D flows.
- Helicity is fundamentally linked to energy transfer, and 2D and 3D properties coexist in all natural flows.
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