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Spectral condensation in laboratory two-dimensional turbulence

Lei Fang1 and Nicholas T. Ouellette2,*

  • 1Department of Civil and Environmental Engineering, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
  • 2Department of Civil and Environmental Engineering, Stanford University, Stanford, California 94305, USA

  • *nto@stanford.edu
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Phys. Rev. Fluids 6, 104605 – Published 19 October, 2021

DOI: https://doi.org/10.1103/PhysRevFluids.6.104605

Abstract

Turbulence in two-dimensional flows is expected to produce a dynamical state in which energy condenses into the largest scale allowed by the system when the scale at which energy is dissipated exceeds the domain size. We study this phenomenon in a laboratory quasi-two-dimensional turbulent flow in a thin layer of electromagnetically driven fluid where the energy is primarily dissipated by bottom friction. By inserting boundaries of different sizes, we fix the driving and damping and vary only the domain size. Although we observe flow patterns that are consistent with previous claims of spectral condensation, we see no signatures in the energy spectrum. An analysis of the scale-to-scale energy flux reveals that small domains weaken the turbulent cascade, even though the bulk forcing and frictional dissipation remain the same. Our results suggest that we lack a robust set of criteria for the existence of spectral condensation, and that claims of condensation in experimental flows with small scale separations must be supported by strong evidence.

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Outline

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Phys. Rev. Fluids 6, 104605– Published 19 October, 2021
  • Received 2 September 2021
  • Accepted 8 October 2021
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