Scaling laws and vortex profiles in two-dimensional decaying turbulence

Area of Science:

• Fluid dynamics
• Turbulence theory
• Computational physics

Background:

• Two-dimensional (2D) decaying turbulence is a fundamental problem in fluid dynamics.
• Understanding vortex statistics is crucial for characterizing turbulent flows.
• Previous theories predicted specific scaling laws for vortex behavior.

Purpose of the Study:

• To investigate the influence of small-scale dissipation on vortex statistics in 2D decaying turbulence.
• To examine the validity of predicted scaling laws under different conditions.
• To analyze the decay of vortex numbers and their spatial distribution.

Main Methods:

• High-resolution numerical simulations of 2D decaying turbulence.
• Analysis of vortex statistics over extended simulation times (hundreds of turnover times).
• Comparison of simulation results with theoretical predictions, including scaling laws and models.

Main Results:

• A scaling regime for vortex statistics was detected when using scaled variables based on mean vorticity and integral scale.
• Viscous effects were observed to disrupt this scaling regime.
• The exponent for the decay of the number of vortices showed a trend towards xi=1, consistent with Kirchhoff model-based theories.
• Scaled vortex profiles exhibited a functional form related to the Fermi-Dirac distribution.

Conclusions:

• Small-scale dissipation significantly influences vortex statistics in 2D decaying turbulence.
• While viscous effects can spoil ideal scaling, the observed trends support existing theoretical frameworks.
• The Fermi-Dirac distribution provides a suitable functional form for describing scaled vortex profiles.