Approximations for turbulent energy and temperature variance dissipation rates in grid turbulence

Abstract

Using a combination of a transverse vorticity (ω3) probe and a pair of parallel cold wires, simultaneous approximations, denoted as εap and εθap, to the energy dissipation rate ε and the temperature variance dissipation rate εθ, are obtained in decaying grid turbulence at a Taylor microscale Reynolds number of about 52. While there are important differences between the spectra of either εap or εθap and those of their isotropic counterparts ε′ and εθ′, the correlation between εap and εθap is as small as that between ε′ and εθ′. The large discrepancies, which exist in the literature, for the correlation coefficient between the locally averaged values of ε and εθ reflect a dependence on the flow type as well as on the Reynolds number. Whereas εap is strongly correlated with ω32, the correlation between ε′ and ω32 is weak. The correlation between εθap and ω32 is comparable to that between εθ′ and ω32. The effect different choices of ε and εθ have on the refined similarity hypothesis (RSH) (Kolmogorov, 1962) and its extension (RSHP) to a passive scalar is also examined. By reference to a nearly complete ε obtained with a three-component vorticity probe, RSH is more closely satisfied by εap than ε′. In contrast, RSHP appears to be approximately satisfied, regardless of which approximations are used for ε and εθ.