4.7 Article

Is grid turbulence Saffman turbulence?

期刊

JOURNAL OF FLUID MECHANICS
卷 642, 期 -, 页码 373-394

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CAMBRIDGE UNIV PRESS
DOI: 10.1017/S0022112009991807

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homogeneous; theory

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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 l, satisfy u(2)l(5) approximate to constant, while in Saffman turbulence we have u(2)l(3) = constant. For strictly homogeneous turbulence the energy decay rates in these two types of turbulence differ, with u(2) similar to t(-10/7) in Batchelor turbulence and u(2) similar to 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)l(3) = constant. The measured energy decay exponent, however, is found to lie slightly below the theoretical prediction of u(2) similar to t(-1/2) Rather we find u(2) similar to t(-n), with n = 1.13 +/- 0.02. This discrepancy is shown to arise from a weak temporal decay of the dimensionless energy dissipation coefficient, is an element of l/u(3), which is normally taken to be constant in strictly homogeneous turbulence, but which varies very slowly in grid turbulence.

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