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

Using a combination of a transverse vorticity (omega(3)) probe and a pair of parallel cold wires, simultaneous approximations, denoted as epsilon(ap) and epsilon(theta ap), to the energy dissipation rate epsilon and the temperature variance dissipation rate epsilon(theta), 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 epsilon(ap) or epsilon(theta ap) and those of their isotropic counterparts epsilon(') and epsilon(theta)('), the correlation between epsilon(ap) and epsilon(theta ap) is as small as that between epsilon(') and epsilon(theta)('). The large discrepancies, which exist in the literature, for the correlation coefficient between the locally averaged values of epsilon and epsilon(theta) reflect a dependence on the flow type as well as on the Reynolds number. Whereas epsilon(ap) is strongly correlated with omega(3)(2), the correlation between epsilon(') and omega(3)(2) is weak. The correlation between epsilon(theta ap) and omega(3)(2) is comparable to that between epsilon(theta)(') and omega(3)(2). The effect different choices of epsilon and epsilon(theta) 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 epsilon obtained with a three-component vorticity probe, RSH is more closely satisfied by epsilon(ap) than epsilon('). In contrast, RSHP appears to be approximately satisfied, regardless of which approximations are used for epsilon and epsilon(theta). (C) 2000 American Institute of Physics. [S1070-6631(00)01001-1].