Generalization of Turbulent Pair Dispersion to Large Initial Separations.

Area of Science:

• Fluid dynamics
• Turbulence research
• Lagrangian mechanics

Background:

• Turbulent pair dispersion describes how particles separate in turbulent flows.
• Existing models often focus on small initial separations.
• Understanding dispersion at large separations is crucial for many applications.

Purpose of the Study:

• To generalize turbulent pair dispersion models to large initial separations.
• To introduce and analyze a new timescale, τ_{v_{0}}, for initial condition persistence.
• To investigate the scaling laws governing pair separation and delay times.

Main Methods:

• Conducting 3D Lagrangian tracking experiments.
• Utilizing moderate Reynolds number flows.
• Conditionally sampling particle pairs based on the new timescale.

Main Results:

• Identified a new timescale, τ_{v_{0}}, relevant for large initial separations.
• Observed Richardson superdiffusive scaling (⟨Δr^{2}⟩∝τ^{3}) for pairs with τ_{v_{0}} shorter than eddy turnover time.
• Determined a ρ^{2/5} scaling for delay times.

Conclusions:

• The new timescale τ_{v_{0}} effectively generalizes turbulent pair dispersion to large separations.
• The findings confirm and extend Richardson's superdiffusive regime.
• The study provides new insights into particle dispersion dynamics in turbulent flows.