展向旋转平面库埃特湍流瞬时场的五分解方法∗

摘要

Spanwise-rotating turbulent plane Couette flow (RPCF) is one of the fundamental prototypes for wall-bounded turbulent flows in rotating reference frames. In this turbulent problem, there are large-scale roll cells which are widely studied. In this paper, a penta-decomposition method is proposed to separate the instantaneous velocity and the total kinetic energy into five parts, i.e., a mean part, a streamwise part and a cross-flow part of the secondary flow, and a streamwise part and a cross-flow part of the residual field. The transport equations for the last four shares, which contribute the total turbulent kinetic energy, are derived. According to these transport equations, the mechanisms of energy transfer among different fractions of turbulent kinetic energy can be revealed clearly. Our objective is to explore the energy balance and transfer among different fractions of the turbulent kinetic energy in RPCF based on a series of direct numerical simulation databases at a Reynolds number Rew=Uwh/ν=1300 (here, Uw is half of the wall velocity difference, and h is the channel half-width) and rotation number Ro = 2Ωzh/Uw (Ωz is the constant angular velocity in the spanwise direction) in a range of 0 6 Ro 6 0.9. The results show that the energy is transferred between the streamwise part/cross-flow part of secondary flows and the residual field through the correlation between the vorticity of secondary flows and the shear stress of residual field. The rotation term acts as a bridge to transfer the energy between the streamwise part and the cross-flow part of either the secondary flows or the residual field. Moreover, pressure-strain redistribution term also plays an important role in the energy transfer between streamwise part and cross-flow part in residual field. For the streamwise part of residual field, in certain rotate rates, the energy obtained from the streamwise part of secondary flows by the correlation between the vorticity of secondary flows and the shear stress of residual field is larger than that obtained from mean flow through mean shear, implying that the streamwise motions of secondary flows have a significant influence on the streamwise motions of residual field.%展向旋转平面库埃特湍流是旋转系统下壁湍流研究的经典问题，并且此湍流问题中的大尺度涡卷(roll cells)结构也受到广泛关注。本文采用五分解方法将存在二次流的瞬时场分解为五部分，包括平均流场、二次流场的流向和横向部分以及剩余场的流向和横向部分。通过五分解法，可以掌握湍动能各分量在能量平衡和能量传递方面的重要机制。研究结果表明：二次流和剩余场的流向运动(横向运动)是通过二次流涡量与剩余场剪应力相关项进行能量传递，二次流(剩余场)的流向运动和横向运动之间是通过旋转项进行能量传递；此外，剩余场的流向和横向运动之间还通过压力与应变率相关的再分配项进行能量传递；对于剩余场流向部分，在一定的旋转强度范围内，通过二次流涡量与剩余场剪应力相关项从二次流流向部分获取的能量大于从平均流获取的能量，说明二次流流向运动对剩余场流向运动有很大影响。