Information production in homogeneous isotropic turbulence

Area of Science:

• Fluid Dynamics
• Turbulence Research
• Nonlinear Dynamics

Background:

• Turbulence is a complex phenomenon characterized by chaotic fluid motion.
• Understanding the scaling laws of turbulence is crucial for many scientific and engineering applications.
• Previous models have not fully captured the behavior of turbulence at different scales.

Purpose of the Study:

• To investigate the Reynolds number (Re) scaling of Kolmogorov-Sinai entropy and attractor dimension in 3D homogeneous isotropic turbulence.
• To compare simulation results with existing theoretical predictions.

Main Methods:

• Direct numerical simulation (DNS) of 3D homogeneous isotropic turbulence.
• Calculation of Lyapunov spectra by tracking the divergence of fluid trajectories.
• Analysis of data across a range of Reynolds numbers.

Main Results:

• The attractor dimension scales with the Reynolds number as Re^{2.35}.
• This observed exponent exceeds predictions from dimensional analysis and intermittency models.
• The distribution of Lyapunov exponents remains finite near zero, challenging Ruelle's divergence hypothesis.

Conclusions:

• The study provides a novel scaling exponent for attractor dimension in turbulence.
• Results highlight the limitations of current theoretical models in describing turbulent dynamics.
• Kolmogorov-Sinai entropy and Lyapunov spectra are valuable tools for comparing complex systems.