Freely Decaying Saffman Turbulence Experimentally Generated by Magnetic Stirrers

Area of Science:

• Fluid Dynamics
• Turbulence Research
• Experimental Physics

Background:

• Homogeneous isotropic turbulence is crucial for testing theoretical models.
• Freely decaying turbulence provides a simplified system for analysis.
• Saffman's and Batchelor's models are key theoretical frameworks for turbulence decay.

Purpose of the Study:

• To experimentally investigate the decay of three-dimensional hydrodynamic turbulence.
• To test the validity of Saffman's and Batchelor's models using experimental data.
• To provide the first experimental evidence for the link between the Saffman invariant and the large-scale energy spectrum.

Main Methods:

• Generating turbulence using magnetic stirrers in a closed container.
• Conducting temporal decay measurements of turbulent kinetic energy and energy dissipation rate.
• Analyzing the growth of the integral scale and the energy spectrum.

Main Results:

• Experimental data strongly support Saffman's model for turbulence decay.
• Conservation of the Saffman invariant was measured at early decay times.
• The energy spectrum was observed to scale as k^2 at large scales and maintain self-similarity.

Conclusions:

• This study provides the first experimental validation of the connection between the Saffman invariant and the k^2-energy spectrum.
• Saffman's model accurately describes the decay regime, especially in large containers.
• The findings advance the understanding of fundamental turbulence dynamics.