Dissipation-range fluid turbulence and thermal noise.

Area of Science:

• Fluid Dynamics
• Statistical Physics
• Turbulence Theory

Background:

• The relevance of thermal fluctuations in incompressible fluid turbulence remains a key question.
• Previous models often assumed deterministic Navier-Stokes equations are sufficient across all scales.

Purpose of the Study:

• To determine the scale at which thermal fluctuations become important in fluid turbulence.
• To assess the validity of deterministic Navier-Stokes equations in the dissipation range.
• To investigate the applicability of fluctuating hydrodynamics equations.

Main Methods:

• Theoretical analysis to estimate the scale of thermal fluctuation relevance.
• Stochastic shell model simulations at high Reynolds numbers.
• Mathematical interpretation of fluctuating Navier-Stokes equations as an effective field theory.

Main Results:

• Thermal fluctuations become significant at the Kolmogorov length, several orders of magnitude above the mean free path.
• Deterministic Navier-Stokes equations are inadequate for describing the dissipation range in molecular fluids.
• Fluctuating hydrodynamics equations are more appropriate, predicting Gaussian thermal equipartition instead of Kraichnan's predictions.
• Simulations confirm theoretical predictions and show inertial-range intermittency can extend into the dissipation range.

Conclusions:

• The deterministic Navier-Stokes equation fails to capture the physics of the dissipation range in molecular fluid turbulence.
• Fluctuating hydrodynamics provides a more accurate description, particularly near the Kolmogorov scale.
• The fluctuating Navier-Stokes equation can be viewed as an effective field theory valid below a certain cutoff.