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This study reveals scaling relations for elastic turbulence (ET) energy and pressure fluctuations. These findings align with polymer stretching dynamics in viscoelastic fluids, validated by experimental and numerical data.

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Area of Science:

  • Fluid Dynamics
  • Rheology
  • Polymer Physics

Background:

  • Elastic turbulence (ET) is a complex flow regime in viscoelastic fluids.
  • Understanding the energy dissipation and fluctuation scaling in ET is crucial for predicting its behavior.

Purpose of the Study:

  • To establish scaling relations for power-law decays of kinetic energy, elastic energy, pressure, and torque fluctuations in elastic turbulence.
  • To investigate the dominant role of the divergent part of elastic stress in polymer stretching within ET.

Main Methods:

  • Theoretical estimation of elastic stress contributions (divergent vs. vortical parts).
  • Analysis of power spectrum amplitudes observed in experimental and numerical studies of ET.
  • Comparison of derived scaling relations with existing experimental and numerical data.

Main Results:

  • Identified scaling relations between exponents of power-law decays for key variables in ET.
  • Demonstrated that the divergent part of elastic stress significantly influences polymer stretching, aligning with theoretical estimates.
  • Confirmed the dominance of the divergent stress component over the vortical component in ET.

Conclusions:

  • The derived scaling relations accurately describe experimental and numerical findings in elastic turbulence.
  • The findings provide a theoretical framework for understanding energy dynamics and polymer behavior in ET.
  • This work contributes to the fundamental understanding of viscoelastic fluid flows and turbulence.