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Dynamic Phase Alignment in Navier-Stokes Turbulence.

Lucio M Milanese1, Nuno F Loureiro1, Stanislav Boldyrev2

  • 1Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.

Physical Review Letters
|January 21, 2022
PubMed
Summary
This summary is machine-generated.

Energy and helicity in Navier-Stokes turbulence cascade together, scaling as k^{-5/3}. This is enabled by a scale-dependent phase alignment between velocity and vorticity fluctuations.

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Area of Science:

  • Fluid dynamics
  • Turbulence theory
  • Statistical mechanics

Background:

  • Navier-Stokes turbulence involves energy and helicity transfer across scales.
  • Understanding the joint cascade of these invariants is crucial for turbulence modeling.
  • Previous studies suggested potential incompatibilities in their simultaneous cascade.

Purpose of the Study:

  • To investigate the spectral scaling of energy and helicity in turbulent flows.
  • To determine the relationship and compatibility between the direct cascades of energy and helicity.
  • To elucidate the underlying mechanism responsible for the joint cascade phenomenon.

Main Methods:

  • Direct numerical simulations (DNS) of Navier-Stokes turbulence.
  • Analysis of spectral energy and helicity transfer rates.
  • Quantification of phase alignment between velocity and vorticity fields.

Main Results:

  • Both energy and helicity exhibit a direct cascade with spectral scaling ∝k^{-5/3}.
  • A strong, scale-dependent phase alignment between velocity and vorticity fluctuations was observed.
  • The phase alignment angle follows the scaling cosα_{k}∝k^{-1}, confirming compatibility.

Conclusions:

  • The joint direct cascade of energy and helicity in Navier-Stokes turbulence is compatible.
  • Scale-dependent phase alignment is the key mechanism enabling the simultaneous cascade.
  • This finding reconciles theoretical predictions and provides insights into turbulent transport processes.