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High-speed Particle Image Velocimetry Near Surfaces
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Published on: June 24, 2013

Exact relation between Eulerian and Lagrangian velocity increment statistics.

O Kamps1, R Friedrich, R Grauer

  • 1Theoretische Physik, Universität Münster, 48149 Münster, Germany.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|August 8, 2009
PubMed
Summary
This summary is machine-generated.

We found a formal link between Lagrangian and Eulerian velocity statistics in turbulence. This connection helps explain non-Gaussian behavior in turbulent flows, applicable across fluid and magnetohydrodynamic systems.

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Area of Science:

  • Physics
  • Fluid Dynamics
  • Plasma Physics

Background:

  • Turbulence exhibits complex statistical properties.
  • Lagrangian and Eulerian descriptions offer different perspectives on fluid motion.
  • Understanding non-Gaussian statistics is crucial for turbulence modeling.

Purpose of the Study:

  • To establish a formal connection between Lagrangian and Eulerian velocity increment distributions.
  • To investigate this connection in the context of two-dimensional turbulence inverse cascades.
  • To identify mechanisms driving non-Gaussian statistics in turbulent flows.

Main Methods:

  • Developing a formal theoretical framework.
  • Numerical estimation of transition probabilities in two-dimensional turbulence.
  • Analysis of velocity increment distributions.

Main Results:

  • A formal connection between Lagrangian and Eulerian velocity increment distributions was established.
  • Numerical estimates for transition probabilities in 2D turbulence inverse cascades were obtained.
  • Direct identification of processes leading to strongly non-Gaussian Lagrangian velocity increments.

Conclusions:

  • The established connection provides a unified approach to analyzing turbulent velocity statistics.
  • The findings are applicable to diverse turbulent systems, including fluids and MHD.
  • This work elucidates the origins of non-Gaussianity in turbulent velocity increments.