On the destruction coefficients for slightly heated decaying grid turbulence

In slightly heated grid turbulence, the mean turbulent kinetic energy and passive-scalar variance dissipation rates, 〈∊〉 and 〈χ〉, decay according to power laws. The isotropic forms of the transport equations for 〈∊〉 and 〈χ〉 suggest that the turbulent mixing (power-law) decay rates depend on the evolution of the ratios G / R λ u and G θ / R λ u , where G and Gθ are the destruction coefficients of 〈∊〉 and 〈χ〉, respectively, and R λ u is the Taylor microscale Reynolds number (λu is the Taylor microscale). The present measurements and previously published data for grid turbulence show that both G and Gθ increase with R λ u but the ratios G / R λ u and G θ / R λ u approach constant values. While G θ / R λ u is nearer to its asymptotic state than G / R λ u , both ratios appear to reach their asymptotic states as R λ u approaches 103. When this occurs, both velocity and scalar fields should be completely self-preserving.