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Lagrangian statistics in weakly forced two-dimensional turbulence.

Michael K Rivera1, Robert E Ecke1

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This study investigates fluid dynamics in a quasi-two-dimensional stratified layer, revealing simultaneous inverse energy and direct enstrophy cascades. These findings offer insights into 2D turbulence dynamics and particle transport.

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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.