Effects of forcing in three-dimensional turbulent flows

Area of Science:

• Fluid Dynamics
• Computational Physics
• Statistical Mechanics

Background:

• Turbulence is a complex phenomenon characterized by chaotic fluid motion.
• Understanding the influence of forcing on turbulent statistics is crucial for theoretical models.
• Previous studies often focused on large-scale forcing, leaving small-scale forcing effects less explored.

Purpose of the Study:

• To numerically investigate the impact of random, power-law spectrum forcing on three-dimensional homogeneous and isotropic turbulence.
• To identify the critical spectrum slope that governs the transition in small-scale turbulent statistics.
• To analyze scaling laws and intermittency under different forcing conditions.

Main Methods:

• Numerical simulations of three-dimensional turbulence.
• Implementation of random forcing with a power-law spectrum E(k) ~ k^(3-y).
• Varying simulation resolution up to 512^3 and spectrum slope 'y' to observe statistical changes.

Main Results:

• A critical spectrum slope, y(c)=4, was identified in three dimensions.
• Below y(c), statistics are forcing-dominated with vanishing intermittency (dimensional scaling).
• Above y(c), anomalous scaling, similar to large-scale forcing, was observed.

Conclusions:

• The spectrum slope of the forcing critically determines small-scale turbulent behavior.
• Results provide insights into the universality of scaling laws in turbulent flows.
• The transition at y(c)=4 highlights the importance of forcing characteristics in turbulence theory.