Pair dispersion and doubling time statistics in two-dimensional turbulence

Area of Science:

• Fluid Dynamics
• Turbulence Theory
• Statistical Mechanics

Background:

• Two-dimensional turbulence exhibits complex energy transfer mechanisms.
• Understanding particle pair separation is crucial for characterizing turbulent flows.
• Stratified-layer systems offer a unique platform for studying turbulence dynamics.

Purpose of the Study:

• To experimentally measure and analyze pair separation statistics in a two-dimensional turbulent system.
• To investigate the distinct scaling behaviors in direct-enstrophy and inverse-energy transfer regimes.
• To compare experimental results with theoretical predictions for turbulent flows.

Main Methods:

• Utilizing an electromagnetically forced stratified-layer system.
• Analyzing experimental data of pair separation as a function of time.
• Employing doubling-time statistics to determine scaling laws.

Main Results:

• Observed exponential scaling of pair separation in the enstrophy transfer range.
• Identified power-law scaling of pair separation in the inverse-energy transfer range.
• Demonstrated agreement between experimental results and theoretical predictions for the doubling-time probability distribution function.

Conclusions:

• Experimental data confirms distinct scaling behaviors in different turbulent regimes.
• Theoretical predictions for exponential and power-law scaling are supported by measurements.
• Finite size effects are significant and must be considered when interpreting turbulent flow data.