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Dynamic multiscaling in two-dimensional fluid turbulence.

Samriddhi Sankar Ray1, Dhrubaditya Mitra, Prasad Perlekar

  • 1Laboratoire Cassiopée, Observatoire de la Côte d'Azur, UNS, CNRS, BP 4229, 06304 Nice Cedex 4, France. samriddhisankarray@gmail.com

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Summary
This summary is machine-generated.

Direct numerical simulations reveal how time scales in 2D fluid turbulence with friction affect multiscaling exponents. Different methods yield distinct exponents, but bridge relations between time-dependent and equal-time exponents hold within error bars.

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Area of Science:

  • Fluid dynamics
  • Turbulence theory
  • Computational physics

Background:

  • Two-dimensional fluid turbulence exhibits complex dynamics, including energy transfer cascades.
  • Air-drag-induced friction introduces dissipation, altering turbulent behavior.
  • Multiscaling analysis is crucial for understanding energy distribution across different scales.

Purpose of the Study:

  • To investigate the impact of friction on the direct-cascade regime in 2D fluid turbulence.
  • To analyze time-dependent and equal-time structure functions of vorticity.
  • To explore the relationship between dynamic-multiscaling exponents and equal-time multiscaling exponents.

Main Methods:

  • Extensive direct numerical simulations were performed.
  • Time-dependent and equal-time structure functions for vorticity were computed.
  • Analyses were conducted in both quasi-Lagrangian and Eulerian frames.
  • Bridge relations between different multiscaling exponents were examined.

Main Results:

  • Different methods for extracting time scales from time-dependent structure functions yield distinct dynamic-multiscaling exponents.
  • These exponents are related to equal-time multiscaling exponents through various bridge relations.
  • The derived bridge relations were verified for a representative friction value within simulation error bars.

Conclusions:

  • The extraction method for time scales significantly influences dynamic-multiscaling exponents in 2D turbulent flows with friction.
  • The established bridge relations provide a consistent framework for connecting time-dependent and equal-time scaling properties.
  • Numerical simulations confirm the validity of these relations, advancing the understanding of dissipative 2D turbulence.