Diffusion of passive scalar in a finite-scale random flow

Area of Science:

• Fluid Dynamics
• Turbulence Theory
• Statistical Mechanics

Background:

• Scalar variance decay is crucial in turbulent flows.
• Understanding spectral properties of decaying scalars is complex.
• Previous models often simplify velocity field interactions.

Purpose of the Study:

• To analyze scalar variance decay in a single-scale random velocity field.
• To elucidate the spectral composition of the
• strange mode
• in decaying turbulence.
• To determine the relationship between decay rate and scale separation.

Main Methods:

• Development of a solvable model for scalar variance decay.
• Analysis of turbulent diffusion effects on scalar modes.
• Investigation of spectral energy transfer across scales.

Main Results:

• Decay rate is proportional to the square of the ratio of box scale to flow scale.
• Transient power-law decay precedes exponential decay.
• Scalar spectra exhibit peaks at box and flow scales, with intermediate power-law behavior.

Conclusions:

• Turbulent diffusion of the largest scales dictates the decay rate.
• The
• strange mode
• combines small-scale features with large-scale decay dynamics.
• The model provides insights into spectral energy distribution in decaying turbulence.