Scale-by-scale Energy Budget Equation In The Far Wake Of Square Cylinder

Scale-by-scale energy budget equation,as a theoretical analysis tool,is an extended form of the Kolmogorov equation.It not only includes small-scale terms such as viscous diffusion and energy transfer,but also considers large-scale terms due to the inhomogeneity of different flow fields.It describes the energy budget of flow fields at different scales.The main purpose of this paper is to analyze scale-by-scale energy budget equation using the experimental data of the far wake of the square cylinder with the Reynolds number of 4000,and explore the energy budget at different lateral positions and different scales.In this paper,the local isotropy is analyzed and proved to be satisfied in the far wake of the square cylinder.The second-order structure function and one-dimensional energy spectrum of longitudinal velocity are analyzed,which prove that the self-preservation is satisfied in the far wake of square cylinder.The energy budget in the far wake of the square cylinder at different scales is obtained by calculating the scale-by-scale energy budget equations of different lateral positions.The self-preservation analysis of the scale-by-scale energy budget equation is performed,and the rates of characteristic velocity scale and characteristic length scale varying with flow direction are 1.45 and 0.36 in the far wake of the square cylinder.The energy budget along the lateral direction y at large scale is obtained by calculating the transport equation for turbulent kinetic energy.The transport equation for the dissipation rate is derived and analyzed in the far wake of the square cylinder.