Energy transfer and dissipation in equilibrium and nonequilibrium turbulence

Abstract

The nonequilibrium dissipation behaviour discovered for decaying fractal square grid-generated turbulence is experimentally investigated using hot-wire anemometry in a wind tunnel. The previous results are consolidated and benchmarked with turbulence generated by regular square-mesh grids, designed to retain certain geometrical parameters of the fractal square grid. This comparison shows that the nonequilibrium behaviour is manifested in both fractal square grid- and regular square-mesh grid-generated turbulence for a downstream region during the turbulence decay up to the first few multiples of the wake interaction distance. For one of the regular grids it is shown that beyond this region there is a transition to the classical dissipation behaviour if the local turbulent Reynolds number is sufficiently high. A sharp conclusion can thus be drawn that this behaviour is more general than initially thought and therefore of much greater scientific and engineering significance. The nonequilibrium dissipation phenomena is further investigated by experimentally measuring the terms of an inhomogeneous von Karman-Howarth-Monin equation. This equation is essentially a scale-by-scale energy transfer budget. From the data it is shown that the inhomogeneity of the turbulent flow does not tamper with the nonequilibrium phenomena and that the scaling of the nonlinear energy transfer, i.e. the transfer of energy to the small-scales, is out of balance with the dissipation. This imbalance leads to the growth of the small-scale advection to compensate for the increasing gap between the energy transferred and the energy dissipated. For the highest Reynolds number data it is also shown that the nonequilibrium dissipation scaling appears to be consistent with the expectation that it is asymptotically independent of the viscosity (as the Reynolds number increases) and that the spectra exhibit a power-law range with the Kolmogorov-Obukhov exponent −5/3. These two observations are shown to be consistent.