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Is grid turbulence Saffman turbulence? (English) Zbl 1183.76749
Summary: There has been a longstanding debate as to whether the large scales in grid turbulence should be classified as of the Batchelor or Saffman type. In the former, the integral scales, \(u\) and \(\ell \), satisfy \(u^{2}\ell ^{5} \approx \) constant, while in Saffman turbulence we have \(u^{2}\ell ^{3} =\) constant. For strictly homogeneous turbulence the energy decay rates in these two types of turbulence differ, with \(u^{2} \sim t^{-10/7}\) in Batchelor turbulence and \(u^{2} \sim t^{-6/5}\) in Saffman turbulence. We present high-resolution measurements of grid turbulence taken in a large wind tunnel. The particularly large test section allows us to measure energy decay exponents with high accuracy. We find that the turbulence behind the grid is almost certainly of the Saffman type, with \(u^{2}\ell ^{3} = \) constant. The measured energy decay exponent, however, is found to lie slightly below the theoretical prediction of \(u^{2} \sim t^{-1.2}\). Rather we find \(u^{2} \sim t^{-n}\), with \(n = 1.13 \pm 0.02\). This discrepancy is shown to arise from a weak temporal decay of the dimensionless energy dissipation coefficient, \(\epsilon \ell /u^{3}\), which is normally taken to be constant in strictly homogeneous turbulence, but which varies very slowly in grid turbulence.

MSC:
76F05 Isotropic turbulence; homogeneous turbulence
Keywords:
homogeneous; theory
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