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Updated: May 16, 2026
13:02
Three-dimensional Particle Tracking Velocimetry for Turbulence Applications: Case of a Jet Flow
Published on: February 27, 2016
Local flow structure of turbulence in three, four, and five dimensions
T Yamamoto1, H Shimizu, T Inoshita
1Department of Physics, Chuo University, 1-13-27 Kasuga, Bunkyo-ku, Tokyo 113-8851, Japan.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 11, 2012
Summary
The smallest eigenvalue in turbulent flows shows wider probability density functions across dimensions, unaffected by dimensionality. This suggests single-direction compression drives intermittent turbulent structures.
Area of Science:
- Fluid Dynamics
- Turbulence Theory
- Computational Physics
Background:
- Incompressible isotropic turbulence is a fundamental concept in fluid dynamics.
- Understanding the behavior of strain tensor eigenvalues is crucial for characterizing turbulence.
- Previous studies have explored turbulence in various dimensions, but multi-dimensional eigenvalue PDFs require further investigation.
Purpose of the Study:
- To compute and analyze the probability density functions (PDFs) of strain tensor eigenvalues for incompressible isotropic turbulence in 3, 4, and 5 dimensions.
- To investigate the influence of spatial dimensions on these PDFs and their relationship to turbulent structures.
- To explore the connection between eigenvalue dynamics and the intermittent structures observed in turbulence.
Main Methods:
- Direct numerical simulation of Navier-Stokes equations.
- Computation of probability density functions (PDFs) for strain tensor eigenvalues.
- Analysis of conditional averages for enstrophy and total squared strain in three dimensions.
Main Results:
- PDFs of the smallest (negative) eigenvalue are consistently wider and dimension-insensitive across all computed dimensions.
- Eigenvalues (excluding the smallest) increase as the smallest eigenvalue decreases, becoming positive for large magnitudes of the smallest eigenvalue.
- Conditional averages of enstrophy and total squared strain increase monotonically with the magnitude of the smallest eigenvalue in 3D.
- The PDF of the pressure Poisson equation source term is positively skewed but tends towards symmetry with increasing spatial dimension.
Conclusions:
- Single-direction compression, driven by the dynamics of the smallest eigenvalue, is proposed as a key factor in generating intermittent turbulent structures.
- The observed dynamics are consistent with Burgers turbulence in d dimensions.
- Dimension effects on the dynamics of the most compressible eigenvalue are significant and warrant further study.
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