Large-scale structure of passive scalar turbulence

Area of Science:

• Fluid Dynamics
• Turbulence Research
• Statistical Mechanics

Background:

• Understanding passive scalar transport in turbulent flows is crucial for various scientific and engineering fields.
• Classical Gibbs equilibrium statistics predict a specific behavior for scalars in the absence of flux, which may not hold under all turbulent conditions.

Purpose of the Study:

• To investigate the large-scale statistical properties of a passive scalar transported by a turbulent velocity field.
• To identify and characterize deviations from classical equilibrium statistics in turbulent scalar transport.
• To explore the underlying mechanisms causing these deviations.

Main Methods:

• Direct numerical simulations (DNS) were employed to model the turbulent velocity field and passive scalar transport.
• Focus was placed on scales larger than scalar injection scales but smaller than velocity correlation lengths.
• Analysis involved examining high-order coarse-grained scalar cumulants to detect long-range correlations.

Main Results:

• The study revealed nontrivial long-range correlations in passive scalar statistics at large scales.
• New power laws were identified for the decay of high-order coarse-grained scalar cumulants.
• These findings contradict the expected Gibbs equilibrium statistics in the absence of scalar flux.

Conclusions:

• The classical Gibbs equilibrium scenario for passive scalar transport is shown to break down at large scales in turbulent flows.
• The statistical geometry of turbulent dispersion, specifically the interaction of scalar blobs, is identified as the cause for this breakdown.
• The obtained scaling exponents align with recent theoretical predictions, validating the simulation results.