Lagrangian statistics in weakly forced two-dimensional turbulence

Area of Science:

• Fluid dynamics
• Turbulence research
• Stratified flow systems

Background:

• Quasi-two-dimensional stratified layer systems are crucial for understanding complex fluid behaviors.
• Electromagnetic forcing injects mean-squared vorticity at specific scales, driving distinct energy and enstrophy cascades.
• Lagrangian statistics provide detailed insights into particle trajectories and fluid motion.

Purpose of the Study:

• To measure Lagrangian single-point and multiple-point statistics in a quasi-two-dimensional stratified layer.
• To analyze the development of simultaneous inverse energy and direct enstrophy cascades.
• To compare Lagrangian and Eulerian velocity statistics and understand scaling behaviors.

Main Methods:

• Utilizing a quasi-two-dimensional stratified layer system (salt water over Fluorinert).
• Employing electromagnetic forcing to inject vorticity at a defined scale.
• Measuring Lagrangian correlations, displacements, velocity fluctuations, energy spectra, and structure functions.
• Comparing Lagrangian data with Eulerian velocity statistics.

Main Results:

• Observed simultaneous cascades: enstrophy to small scales, energy to larger scales.
• Characterized Lagrangian behavior based on trapping near centers and saddles.
• Found that spectral inverse energy and enstrophy ranges are not directly mirrored in real-space moments.
• Noted alignment between spectral ranges and moment ratios, indicating changes in probability distribution functions.

Conclusions:

• The study elucidates the complex interplay of energy and enstrophy cascades in stratified 2D turbulence.
• Lagrangian measurements reveal the influence of topological structures on particle motion.
• Discrepancies between spectral and real-space statistics highlight the nuances of scaling in turbulent flows.
• Findings contribute to a deeper understanding of weakly forced 2D turbulence with dual cascade phenomena.