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Quad-Decomposition of Velocity Field in Spanwise-Rotating Turbulent Plane Couette Flows

Abstract In this paper, we propose a new quad-decomposition approach for the instantaneous flow field which has the secondary flows. Different from the previously reported quad-decomposition, where the velocity field is decomposed into a mean part, a streamwise part and a cross-flow part of the secondary flow, and the residual three-dimensional fluctuation part, our new quad-decomposition separates the flow field into a mean part, a streamwise streaks-related part, a cross-flow roll-cells-related part and a residual cross-flow fluctuation part. These two decomposition approaches are used to explore the underlying physics of the energy balance and transfer among different shares of the turbulent kinetic energy in spanwise-rotating turbulent plane Couette flows. The new quad-decomposition can provide clear pictures of the energy transfer from the streaks to the residual cross-flow fluctuations due to the system rotation and the correlation between pressure and streamwise velocity fluctuations’ gradient, in addition to the bridge role of the cross-flow roll-cells-related field between the mean field and the residual fluctuation field, which can also be demonstrated by the previous quad-decomposition.