%0 Journal Article %1 liu2001largescale %A Liu, Z. %A Adrian, R. J. %A Hanratty, T. J. %D 2001 %I Cambridge University Press %J Journal of Fluid Mechanics %K 76f10-turbulent-shear-flows 76f25-turbulent-transport-mixing %P 53-80 %R 10.1017/S0022112001005808 %T Large-scale modes of turbulent channel flow: transport and structure %U https://www.cambridge.org/core/article/largescale-modes-of-turbulent-channel-flow-transport-and-structure/99FDD3632F90830BA91440A94E8486B8 %V 448 %X 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.

@article{liu2001largescale, abstract = {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.}, added-at = {2024-03-10T23:44:31.000+0100}, author = {Liu, Z. and Adrian, R. J. and Hanratty, T. J.}, biburl = {https://www.bibsonomy.org/bibtex/2a15388b784a248a8ef2bd46067843bc9/gdmcbain}, doi = {10.1017/S0022112001005808}, interhash = {16370ddf539950e0422b5e170328a895}, intrahash = {a15388b784a248a8ef2bd46067843bc9}, issn = {00221120}, journal = {Journal of Fluid Mechanics}, keywords = {76f10-turbulent-shear-flows 76f25-turbulent-transport-mixing}, pages = {53-80}, publisher = {Cambridge University Press}, timestamp = {2024-03-10T23:44:31.000+0100}, title = {Large-scale modes of turbulent channel flow: transport and structure}, url = {https://www.cambridge.org/core/article/largescale-modes-of-turbulent-channel-flow-transport-and-structure/99FDD3632F90830BA91440A94E8486B8}, volume = 448, year = 2001 }