Turbulent flow in a rectangular channel is investigated to determine the scale and
pattern of the eddies that contribute most to the total turbulent kinetic energy and
the Reynolds shear stress. Instantaneous, two-dimensional particle image velocimeter
measurements in the streamwise-wall-normal plane at Reynolds numbers Reh = 5378
and 29 935 are used to form two-point spatial correlation functions, from which
the proper orthogonal modes are determined. 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 large fraction of the kinetic energy of the streamwise velocity
component and a small fraction of the kinetic energy of the wall-normal velocities.
Surprisingly, the set of large-scale modes that contains half of the total turbulent
kinetic energy in the channel, also contains two-thirds to three-quarters 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. Samples of the large-scale structures associated with
the dominant eigenfunctions are found by projecting individual realizations onto the
dominant modes. In the streamwise wall-normal plane their patterns often consist
of an inclined region of second quadrant vectors separated from an upstream region
of fourth quadrant vectors by a stagnation point/shear layer. The inclined Q4/shear
layer/Q2 region of the largest motions extends beyond the centreline 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 hairpin vortex. Reynolds number similarity of the
large structures is demonstrated, approximately, by comparing the two-dimensional
correlation coefficients and the eigenvalues of the different modes at the two Reynolds
numbers.
Measurement of Beacon Anisoplanatism Through a Two-Dimensional Weakly-Compressible Shear Layer
