Pair dispersion in synthetic fully developed turbulence

Area of Science:

• Fluid Dynamics
• Turbulence Theory
• Statistical Mechanics

Background:

• Lagrangian statistics describe particle movement in turbulent flows.
• Understanding relative dispersion is key to predicting turbulent transport.
• Previous models often simplified turbulence dynamics.

Purpose of the Study:

• To numerically investigate Lagrangian statistics of relative dispersion in fully developed turbulence.
• To explore the impact of intermittency on scaling laws.
• To validate theoretical predictions against numerical simulations.

Main Methods:

• Numerical simulation of a two-dimensional velocity field.
• Utilizing a stochastic process and a dynamical shell model.
• Analysis based on fixed scale statistics for extended scaling ranges.

Main Results:

• Lagrangian statistics exhibit self-similarity under Kolmogorov similarity conditions, matching Richardson's predictions.
• Intermittent velocity fields lead to scaling laws dependent on Eulerian intermittency, consistent with multifractal descriptions.
• The variance of pair separation follows Richardson's law, unaffected by intermittency corrections.
• Lagrangian exponents are independent of specific Eulerian dynamics.

Conclusions:

• Kolmogorov's theory and Richardson's law are robust even in intermittent turbulence.
• Multifractal analysis accurately describes scaling laws in intermittent fields.
• Fixed scale statistics offer a superior method for analyzing experimental turbulence data.