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Fractally Fourier decimated homogeneous turbulent shear flow in noninteger dimensions
1Department of Aerospace Engineering, K.N. Toosi University of Technology, Tehran, Iran.
Physical Review. E
|March 17, 2017
Summary
Investigating turbulent shear flow in noninteger Fourier dimensions reveals that decreasing the dimension hampers energy distribution and suppresses forward energy transfer, impacting turbulence dynamics.
Area of Science:
- Fluid Dynamics
- Turbulence Theory
- Computational Physics
Background:
- Turbulent shear flows are fundamental in fluid dynamics, exhibiting complex dynamics across multiple scales.
- Understanding energy transfer mechanisms is crucial for characterizing turbulence.
- Previous studies primarily focused on integer (3D) spatial dimensions.
Purpose of the Study:
- To numerically investigate the time evolution of incompressible homogeneous turbulent shear flow in noninteger Fourier dimensions.
- To analyze the influence of varying Fourier dimensions (2.7 ≤ d ≤ 3.0) on turbulence characteristics.
- To examine how noninteger dimensions affect energy distribution, anisotropy, and spectral transfer.
Main Methods:
- Numerical simulation of the Navier-Stokes equation projected onto fractal sets of active Fourier modes.
- Extension of the Fourier dimension from integer 3 to noninteger values (2.7 to 3.0).
- Analysis of turbulent production, dissipation, energy distribution, anisotropy, vortex stretching, and spectral energy transfer.
Main Results:
- Decreasing Fourier dimension (d) significantly hampers turbulent production and dissipation, while their ratio remains largely independent of d.
- Energy distribution among spatial directions is impeded as d decreases, leading to increased large-scale anisotropy.
- Forward spectral energy transfer and vortex stretching mechanisms are suppressed at lower d, reducing intermittency and deviation from Gaussianity.
- Nonlocal triadic interactions' contribution to kinetic energy exchange increases with increasing Fourier dimension.
Conclusions:
- Noninteger Fourier dimensions significantly alter the dynamics of turbulent shear flow.
- The study highlights the sensitivity of turbulence characteristics to the dimensionality of the Fourier space.
- Findings suggest that extending turbulence studies to noninteger dimensions offers new insights into energy transfer and scaling laws.
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