Langevin based turbulence model and its relationship with Kappa distributions

Area of Science:

• Physics
• Statistical Mechanics
• Fluid Dynamics

Background:

• Complex phenomena with high degrees of freedom, like turbulent systems, are often analyzed using non-extensive statistical mechanics.
• Kappa distributions (κ-like distributions) provide a robust framework for characterizing such phenomena.

Purpose of the Study:

• To analyze the relationship between turbulent flow, spatial scale dynamics, and κ-like distributions.
• To investigate the connection between the κ parameter, scale, and Reynolds number (Re) in turbulent systems.

Main Methods:

• Utilized a coupled map lattice Langevin-based model.
• Generated steady-state velocity distributions of fluid at various spatial scales.
• Fitted the generated distributions using κ-like distributions.

Main Results:

• Generated fluid velocity distributions were well-fitted by κ-like distributions across different scales.
• Observed a robust relationship between the κ parameter, spatial scale, and the Reynolds number (Re).
• Established a closed scaling relation between turbulence level and the κ parameter: κ ∝ Re^(3/2).

Conclusions:

• κ-like distributions are effective for modeling turbulence across different spatial scales.
• The established scaling relation provides a quantitative link between turbulence intensity and the κ parameter.
• Numerical predictions are available for experimental validation in diverse turbulent flow contexts.