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Interscale energy transfer in decaying turbulence and vorticity–strain-rate dynamics in grid-generated turbulence

For decaying homogeneous turbulence, we present two assumptions about the energy spectrum and one on the dissipation rate coefficient Cϵ which, in a high inlet/initial Reynolds number limit, imply that a wide range of wavenumbers exists where the interscale energy flux is dependent on inlet/initial Reynolds number, is negative (kinetic energy is on average transferred from small to high wavenumbers) and is independent of wavenumber but not necessarily of viscosity. Our assumptions about the energy spectrum are not unusual, one concerns the finite nature of the energy and the other its time dependence, and our assumption about Cϵ is inspired by recent wind tunnel and water channel measurements of turbulence generated by fractal and regular grids. We then present a direct numerical simulation of fractal-generated turbulence where the second-order structure function in time exhibits a well-defined 2/3 power law over more than a decade at a position close to the grid where the local Reynolds number Reλ is only about 30 and where there is neither average production of enstrophy nor of strain rate. The Q–R and Qs–Rs diagrams do not have their usual appearance at this position but develop it gradually as the flow progresses downstream and the wide 2/3 power law of the second-order structure function is eroded. It is believed that this is the first time that the spatial development of Q, R, Qs and Rs statistics is obtained for a spatially developing turbulent flow.