Scaling of the turbulent energy dissipation correlation function. (25th May 2020) - Tang, S. L.
Abstract : Abstract : We examine the scaling of the two-point correlation function for $\unicode[STIX]{x1D716}$, the energy dissipation rate, over a range of values of the separation $r$ between the two points and the Taylor microscale Reynolds number $Re_{\unicode[STIX]{x1D706}}$ . The correlation function is estimated from hot-wire measurements in grid turbulence, along the axes of wakes and jets, and along the centreline of a fully developed channel flow. When $Re_{\unicode[STIX]{x1D706}}$ exceeds a value of approximately 300, a condition which is achieved for both plane and circular jets, the correlation function collapses over nearly all values of $r$ when the normalization uses Kolmogorov scales. However, there is no collapse in either the power-law range or dissipative range when the normalization is on the integral (or external) length scale, which indicates that there is no self-similarity based on external scales. Although the maximum value of $Re_{\unicode[STIX]{x1D706}}$ is not much larger than $10^{3}$, the behaviour of the energy dissipation correlation function on the axes of plane and circular jets seems consistent with the first similarity hypothesis of Kolmogorov ( Dokl. Akad. Nauk SSSR, vol. 30, 1941, pp. 299–303) but not with the revised phenomenology of Kolmogorov ( J. Fluid Mech., vol. 13, 1962, pp. 82–85).