Coherent Structures In Turbulent Channel Flows

With advances in experimental and computational techniques, various coherent structures have been identified in turbulent channel flows. These coherent structures offer clues to understand the fundamental turbulent physics and hold the key to modeling andcontrolling turbulent phenomena.Vortices constitute one typical category of coherent structures, and the swirlingstrength has been widely used as an effective vortex indicator. Available swirling-strength methods involve merely numerical solutions for vortex identification, failing to provide insight into parametric dependency of the swirling strength. The use of 2D and 3D swirling strengths for vortex extraction also leads to varying or even contradicting evidence in vortex character. A comprehensive comparison is still lacking of the vortices extracted in three orthogonal planes.Analytic solutions of swirling strength ispresentedby solving the characteristic equation of the local velocity gradient tensor. Based on the analytic solutions, three important aspects are investigated, including the influence of mean shear on vortex identification, the difference between 2D and 3D vortices, and the characteristics of cavity flows. Major findings are as follows:(1) The 2D and 3D swirling strengths are analytically related. The 3D swirling strength comprises of three components, namely, the 2D swirling, the local compactness, and the extensional strains.Statistics based on DNS data show these three components contribute 84%, 5% and 11%, respectively, to the 3D swirling strength. The elevation anglea, made by the vortex orientation with the measured plane, determines the difference between 2D and 3D swirling strengths, (2)The mean shear affects vortex identification through . Vortex identification is hindered when a vortex rotates in the opposite sense to the mean shear which is larger than one-half of the vorticity at the vortex center. Fortunately, such condition occurs predominantly in the region ofy+<50.(3) The density of 2D vortices exceeds that of 3D vortices as the 2D approachtends to break a 3D vortex into several 2D pieces. The in-plane radius of 2D vortices is less than that of 3D vortices, while it is greater than the tube radius of 3D vortices. Elevation angles made with XY, YZ and XZ planes mainly distribute in the range of 45°~55°. The JPDF between elevation angle and projection angle indicates that vortices orient orderly in the inner layer, while they turn into random orientations in the outer layer.(4) In a cavity flow, the shear layer impinges on the trailing edge, the trailing wall and the cavity bottom after separation from the leading edge. Based on results of gyres, Reynolds stress, vortices and POD modes, a phenomenological model of coherent structures in cavity flows is proposed to predict the location of retardation and sedimentation of pollution inside the cavity.