Velocity Space-Time Correlations in Turbulent Thermal Convection
Turbulent kinetic energy cascades are of prime importance and have been the central issue in the study of fluid tur-bulence. An important quantity to describe such cascade processes is the velocity space-time correlation functionC(r;t ) = <v(x+r; t +t )v(x; t)>=vrms(x)vrms(x+r). Based on a second order approximation to C(r;t ), He & Zhang ”1”advanced an elliptic model and proposed that C(r;t ) could be related to C(rE;0) via r2E = (r-Ut )2+V2t 2, where Uand V are the convection and sweeping characteristic velocities, respectively. The He”s elliptic model provides a usefultool for a large set of flow systems where the Taylor”s hypothesis does not hold and hence the validity of the model invarious practical flows of interest needs to be tested.In this paper, we want to validate the elliptic model in turbulent convection ”2”. The flow at hand is turbulent Rayleigh-B?enard (RB) convection, i.e. the convective motion of an enclosed fluid layer heated from below and cooled fromabove, which has received tremendous attention during the past few decades ”3”. The two-dimensional velocity fieldin the vertical plane of the large-scale circulation in a water-filled cylindrical turbulent RB convection cell of height 50cm and unit aspect ratio was measured via the particle image velocimetry (PIV) technique ”4”. Figures 1(a) and (b)show the isocorrelations contours of the measured C(r;t ). It is seen that the contours are elliptic closed curves. Themeasured values of |U| and V are plotted in figure 1(c). One sees that |U| and V are approximately the same near thecell sidewall, while V -0 at the cell center. All these results indicate that while the Taylor”s hypothesis does not holdin turbulent thermal convection, the elliptic model is valid for the present velocity field for all over the cell.
Quan ZHOU
Shanghai Institute of Applied Mathematics and Mechanics,Shanghai University,Shanghai 200072,China
国内会议
第十三届现代数学和力学学术会议(MMM-XIII)暨钱伟长诞辰100周年纪念大会
上海
英文
1
2012-10-05（万方平台首次上网日期，不代表论文的发表时间）