Correlation Measurement in a Turbulent Flow using High-Speed Computing Methods

Abstract

Third‐order time‐correlations downstream of a grid were measured with a hot‐wire anemometer using high‐speed computing methods. The nonlinear response of the hot‐wire to the fluctuations of velocities is taken into account as well as the effect of transverse velocities. It is found that the correlations $R_t^{\text{2,1}}\mathrm{(h)=}\overline{{\mathrm{u\prime }}^2\mathrm{(t)u\prime (t+h)}}/{\overline{{\mathrm{(u\prime }}^2)}}^{\text{3/2}}$ and $R_t^{\text{1,2}}\mathrm{(h)=}\overline{{}^u{\mathrm{\prime (t)u\prime }}^2\mathrm{(t+h)}}/{\overline{{\mathrm{(u\prime }}^2)}}^{\text{3/2}}$ are substantially different from previous results and demonstrate that the assumption of isotropy is not adequate for these correlations downstream of a grid. The nonlinear response does not significantly affect the difference ½(R_t^2,1 − R_t^1,2). Since previous conclusions concerning the nature of third‐order correlations were based on the measurements of such differences they masked the effects of nonlinearity on the individual correlations. Correlations of fifth‐order are also presented and their relations to the third‐order correlation are discussed. Although the nonlinear corrections are quite important for odd‐order correlations they are negligible for correlations of even‐order.