Temperature correlations with vorticity and velocity in a turbulent cylinder wake

Abstract

This work aims to understand the difference in the correlations between the fluctuating temperature and the vorticity from that between the fluctuating temperature and the velocity in a turbulent cylinder near wake. Measurements are made at x/d = 10, 20 and 40, where x is the streamwise distance from the cylinder axis and d is the cylinder diameter, with a Reynolds number of 2.5×103 based on d and the free-stream velocity. The three components of the fluctuating velocity vector ui(i = 1, 2 and 3), vorticity vector ωi (i = 1, 2 and 3), and temperature θ in the plane of the mean shear are measured simultaneously with a multi-wire probe consisting of four X-hotwires and four cold wires. It is found that at x/d = 10, both correlations between uiand θ and between ωi and θ predominantly take place at St = 0.21, due to the concentric distribution of the Kármán vortices and the heat. With increasing x/d, the correlation between ωi (i = 1, 2 and 3) and θ drops rapidly, as a result of the weakened Kármán vortices; in contrast, the correlation between u1 and θ increases appreciably, largely due to an enhanced correlation between u1 and θ at low frequencies or scales of motions larger than the Kármán vortex. The slowly decreasing (along x) two-point autocorrelations of u1 and θ suggest that the very-large-scale motions (VLSMs) found in wall flows occur also in the turbulent wake and are responsible for the high correlation between u1 and θ at low frequencies.