Kármán-Howarth closure equation on the basis of a universal eddy viscosity.

This Rapid Communication presents a simple closure for the two-point correlation transport equation in decaying isotropic turbulence. It relies essentially on an eddy viscosity ν(t) which exhibits some remarkable universal facets over an impressively wide range of scales. This allows us to model the third-order structure functions in different decaying flows covering a large extent of Reynolds numbers. The model is numerically time integrated to predict the decay of second-order structure functions and compared to experiments in grid turbulence. Agreement between predictions and measurements is satisfactory.

Power law of decaying homogeneous isotropic turbulence at low Reynolds number.

We focus on an estimate of the decay exponent (m) in the initial period of decay of homogeneous isotropic turbulence at low Taylor microscale Reynolds number R lambda (approximately equal to 20-50). Lattice Boltzmann simulations in a periodic box of 256(3) points are performed and compared with measurements in grid turbulence at similar R lambda. Good agreement is found between measured and calculated energy spectra. The exponent m is estimated in three different ways: from the decay of the turbulent kinetic energy, the decay of the mean energy dissipation rate, and the rate of growth of the Taylor microscale. Although all estimates are close, as prescribed by theory, that from the Taylor microscale has the largest variability. It is then suggested that the virtual origin for the decay rate be determined from the Taylor microscale, but the actual value of m be estimated from the decay rate of the kinetic energy. The dependence of m on R lambda(0) (the value of R lambda at the beginning of the simulation) is also analyzed, using the present data as well as data from the literature. The results confirmed that m approaches 1, as R lambda(0) increases.