Large-scale modes of turbulent channel flow: transport and structure

Turbulent flow in a rectangular channel is investigated to determine the sc ale and pattern of the eddies that contribute most to the total turbulent k inetic energy and the Reynolds shear stress. Instantaneous, two-dimensional particle image velocimeter measurements in the streamwise-wall-normal plan e at Reynolds numbers Re-h = 5378 and 29935 are used to form two-point spat ial correlation functions, from which the proper orthogonal modes are deter mined. Large-scale motions-having length scales of the order of the channel width and represented by a small set of low-order eigenmodes-contain a lar ge fraction of the kinetic energy of the streamwise velocity component and a small fraction of the kinetic energy of the wall-normal velocities. Surpr isingly, the set of large-scale modes that contains half of the total turbu lent kinetic energy in the channel, also contains two-thirds to three-quart ers of the total Reynolds shear stress in the outer region. Thus, it is the large-scale motions, rather than the main turbulent motions, that dominate turbulent transport in all parts of the channel except the buffer layer. S amples of the large-scale structures associated with the dominant eigenfunc tions are found by projecting individual realizations onto the dominant mod es. In the streamwise wall-normal plane their patterns often consist of an inclined region of second quadrant vectors separated from an upstream regio n of fourth quadrant vectors by a stagnation point/shear layer. The incline d Q4/shear layer/Q2 region of the largest motions extends beyond the centre line of the channel and lies under a region of fluid that rotates about the spanwise direction. This pattern is very similar to the signature of a hai rpin vortex. Reynolds number similarity of the large structures is demonstr ated, approximately, by comparing the two-dimensional correlation coefficie nts and the eigenvalues of the different modes at the two Reynolds numbers.