On invariants in grid turbulence at moderate Reynolds numbers

The decay characteristics and invariants of grid turbulence were investigated by means of laboratory experiments conducted in a wind tunnel. A turbulence-generating grid was installed at the entrance of the test section for generating nearly isotropic turbulence. Five grids (square bars of mesh sizes $M= 15$ , 25 and 50 mm and cylindrical bars of mesh sizes $M= 10$ and 25 mm) were used. The solidity of all grids is σ = 0. 36 . The instantaneous streamwise and vertical (cross-stream) velocities were measured by hot-wire anemometry. The mesh Reynolds numbers were adjusted to ReM = 6700 , 9600, 16 000 and 33 000. The Reynolds numbers based on the Taylor microscale Reλ in the decay region ranged from 27 to 112. In each case, the result shows that the decay exponent of turbulence intensity is close to the theoretical value of - 6/ 5 (for the M= 10~mm grid, - 6(1+ p)/ 5~ - 1. 32 ) for Saffman turbulence. Here, p is the power of the dimensionless energy dissipation coefficient, A(t)~ tᵖ . Furthermore, each case shows that streamwise variations in the integral length scales, Lᵤᵤ and Lᵥᵥ , and the Taylor microscale λ grow according to Lᵤᵤ ~ 2Lᵥᵥ ∝ (x/ M- x₀ / M)2/ 5 (for the M= 10~mm grid, Lᵤᵤ ∝ (x/ M- x₀ / M)2(1+ p)/ 5 ~ (x/ M- x₀ / M)0. 44 ) and λ ∝ (x/ M- x₀ / M)1/ 2 , respectively, at x/ M> 40x2013 60 (depending on the experimental conditions, including grid geometry), where x is the streamwise distance from the grid and x₀ is the virtual origin. We demonstrated that in the decay region of grid turbulence, uᵣₘₛ² Lᵤᵤ³ and vᵣₘₛ² Lᵥᵥ³ , which correspond to Saffman’s integral, are constant for all grids and examined ReM values. However, uᵣₘₛ² Lᵤᵤ⁵ and vᵣₘₛ² Lᵥᵥ⁵ , which correspond to Loitsianskii’s integral, and uᵣₘₛ² Lᵤᵤ² and vᵣₘₛ² Lᵥᵥ² , which correspond to the complete self-similarity of energy spectrum and u² ~ t- 1 , are not constant. Consequently, we conclude that grid turbulence is a type of Saffman turbulence for the examined ReM range of 6700–33 000 ( <jats:inline-graphic xmlns:xlink="http: