Energy dissipation and enstrophy production/destruction at very low Reynolds numbers in the final stage of the transition period of decay in grid turbulence

Abstract

Decay characteristics of turbulent kinetic energy and enstrophy in grid turbulence have been investigated in the far downstream region (x / M ∼ 10 3: x is the downstream distance from the grid, M is the mesh size of the grid) through wind tunnel experiments using hot-wire anemometry, with the lowest turbulent Reynolds number R e λ ≈ 5. The non-dimensional dissipation rate C ϵ increases rapidly toward the final stage of the transition period of decay and the profile agrees well with previous direct numerical simulation [W. D. McComb et al., "Taylor's (1935) dissipation surrogate reinterpreted,"Phys. Fluids 22, 061704 (2010)] and theoretical estimation [D. Lohse, "Crossover from high to low Reynolds number turbulence,"Phys. Rev. Lett. 73, 3223 (1994)] at very low R e λ in decaying and stationary isotropic turbulence. The present result of C ϵ is an update on the experimental data in grid turbulence toward a very low R e λ, where measurements have been absent. The energy spectrum in the dissipation range at very low R e λ deviates from a universal form observed at high Reynolds numbers. The decay rate of enstrophy is proportional to S + 2 G / R e λ (S is the skewness of the longitudinal velocity derivative and G is the destruction coefficient). It is shown that G and S + 2 G / R e λ increase rapidly with decreasing R e λ at very low R e λ, indicating that the effect of enstrophy destruction is dominant in the final stage of the transition period of decay. The profiles of S + 2 G / R e λ against R e λ is well fitted by a power-law function even in the final stage of the transition period of decay.