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Three-dimensional Particle Tracking Velocimetry for Turbulence Applications: Case of a Jet Flow
Published on: February 27, 2016
Hyperviscosity, Galerkin truncation, and bottlenecks in turbulence
Uriel Frisch1, Susan Kurien, Rahul Pandit
1Laboratoire Cassiopée, OCA, UNS, CNRS, BP 4229, 06304 Nice cedex 4, France.
Physical Review Letters
|October 15, 2008
Summary
High power alpha in hydrodynamics leads to truncated inviscid dynamics. Large wave numbers thermalize, while small wave numbers exhibit viscous behavior, suggesting incomplete thermalization.
Area of Science:
- Fluid dynamics
- Statistical mechanics
- Computational physics
Background:
- Hydrodynamical equations govern fluid motion.
- Dissipative terms model energy loss.
- Laplacian operators are used in differential equations.
Purpose of the Study:
- Investigate the asymptotic behavior of hydrodynamical equations with a high power alpha Laplacian in the dissipative term.
- Analyze the resulting dynamics and spatial Fourier mode behavior.
- Interpret the energy bottleneck phenomenon and discuss model artifacts.
Main Methods:
- Asymptotic analysis of hydrodynamical equations.
- Study of spatial Fourier modes.
- Numerical or analytical investigation of the dissipative term with high power alpha Laplacian.
Main Results:
- Asymptotic dynamics become truncated inviscid conservative dynamics.
- A finite range of spatial Fourier modes is observed.
- Modes at large wave numbers thermalize.
- Modes at small wave numbers exhibit ordinary viscous dynamics.
- Energy bottleneck for finite alpha indicates incomplete thermalization.
Conclusions:
- The model with high power alpha Laplacian leads to a transition from viscous to inviscid dynamics.
- Incomplete thermalization is a key feature for finite alpha.
- Artifacts in models with alpha > 1 require careful consideration.
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