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Optical technique for direct measurement of power spectra in compressible turbulence

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Abstract

We present exploratory tests of a new optical method which measures directly two components of the 3-D power spectrum of the refractive-index fluctuation. The method was applied to a Mach 2 turbulent shear layer. Length scales of 0.1 mm to 1.0 mm were resolved within a shear-layer thickness ranging from 5 mm to 10 mm. At low-to-moderate wavenumbers, the spectral behavior is roughlyκ −3, while at higher wavenumbers it isκ −3.7. These spectral slopes are in agreement with prevailing theoretical predictions for anisotropic (low-wavenumber) and isotropic (high-wavenumber) turbulence.

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Abbreviations

a :

speed of sound

l :

eddy size

n :

refractive index

S :

mean strain rate

S h :

mean shear

T :

static temperature

U :

freestream velocity

x :

axial direction

y :

transverse direction

z :

spanwise direction

δ :

shear-layer thickness

δ′:

=dδ/dx: growth rate

ɛ :

viscous dissipation

ΔU :

=U 1−U 2

κ :

wavenumber

ϱ :

density

Φ :

3-D power spectrum

1:

fast stream

2:

slow stream

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Author information

Authors and Affiliations

  1. Dept. of Aerospace & Mechanical Engineering, University of California, 92717, Irvine, CA, USA

    D. Papamoschou

  2. Lawrence Livermore National Laboratory, P.O. Box 808, 94550, Livermore, CA, USA

    H. F. Robey

Authors
  1. D. Papamoschou
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  2. H. F. Robey
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Additional information

]This study was funded by a grant from Lawrence Livermore National Laboratory and by a grant from the California Space Institute. DP is indebted to HFR and Dr. Alfred C. Buckingham of LLNL for their support.

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Papamoschou, D., Robey, H.F. Optical technique for direct measurement of power spectra in compressible turbulence. Experiments in Fluids 17, 10–15 (1994). https://doi.org/10.1007/BF02412798

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