Organization and scaling of coherent structures in the outer region of high-Reynolds-number turbulent boundary layers A DISSERTATION SUBMITTED TO THE FACULTY OF THE UNIVERSITY OF MINNESOTA BY Michael Heisel IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY Michele Guala May 2020 © 2020 Michael Heisel Acknowledgements Perhaps contrary to the spirit of a dissertation, my doctoral thesis research was not the outcome of a singular individual effort. The name on the cover and the words on the following pages are my own, but this thesis is the outcome of collective contributions from many wonderful colleagues. Foremost to thank is my advisor Professor Michele Guala. Beyond the mechanics of how to conduct experiments, he taught me how to approach turbulence research as an art in order to untangle meaning from the chaos. He also spent countless hours providing feedback and guidance, and is most responsible for my development as a researcher. To encapsulate my feelings I must invoke the words of Tina Turner: you’re simply the best, better than all the rest. The experiments presented here, and those not included in the thesis, were conducted at St. Anthony Falls Laboratory (SAFL). The construction and setup of the experiments in many cases were carried out by the skillful engineering staff at SAFL. Specifically, my work was directly or indirectly facilitated by Chris Feist, Chris Milliren, Dr. Chris Ellis, Jim Tucker, Erik Steen, Aaron Ketchmark, and Ben Erickson. They spared me from scrapes and bruises and prevented further destruction of the wind tunnel facility. I would also like to thank the IT staff (Charles Nguyen, Patrick Arnold, Matt Jansen, among others) for their help with all things computer, including maintenance of the high-performance computing resources used for data processing. My research was continuously advanced through the input of several faculty at the University of Min- nesota. Professors Jiarong Hong and Filippo Coletti provided insight as co-investigators on the atmospheric study during both group meetings and independent conversations. I am grateful to Drs. Hong and Coletti, in addition to Professors Vaughan Voller and Ellen Longmire, for serving on my doctoral exam committee and providing valuable feedback to this work. I have benefited from several rewarding relationships outside of Minnesota. Much of my thesis relies on the output of a collaboration with the University of Melbourne. I am grateful to Professors Charitha de Silva, Nicholas Hutchins, and Ivan Marusic for contributing their time, experimental data, and expertise to help bring this work to fruition. I would also like to thank Professor Gabriel Katul of Duke University for his mentorship. While the findings of our ongoing collaboration are not represented in this thesis, Dr. Katul has been invaluable to the development of my future research goals and professional career. Finally, and this work would not have been possible without sponsorship. The following organizations have funded my various research projects as a graduate student: the National Science Foundation, the Institute on the Environment, the Minnesota Department of Transportation, and the Graduate School at the University of Minnesota. i Dedication to Papa Bear ii Abstract Recent advances in high-Reynolds-number turbulence have suggested there is a general self-organization of coherent structures in the logarithmic and wake regions of boundary layer flows. The organization com- prises large-scale velocity structures known as uniform momentum zones (UMZs) separated by thin internal shear layers (ISLs). While the velocity structures have been extensively studied in more specific forms such as momentum streaks, streamwise rolls, and bulges, the shear layers have received less attention outside the context of the hairpin packet paradigm. In the present thesis, the universality of this self-organization is eval- uated using a novel field-scale particle image velocimetry (PIV) experiment in the logarithmic region of the atmospheric surface layer. The field measurements are validated using collocated sonic anemometry. The experiment reveals the same organization of UMZs and ISLs occurs for atmospheric flows. The properties of the UMZs and ISLs are then compared using ten PIV experiments and a direct numerical simulation, which together span a wide range of surface roughness and three orders of magnitude in Reynolds number. The UMZs unambiguously scale with the friction velocity and wall-normal distance in the logarithmic region, regardless of Reynolds number and surface roughness. The scaling behavior is in agreement with Prandtl’s mixing length theory and Townsend’s attached eddy hypothesis. The results show that the hypothetical eddies of the logarithmic law of the wall manifest in the structural organization of the flow. Separate analysis focus- ing on the smaller structures shows that the ISLs and large vortices are both governed by the friction velocity and Taylor microscale. Preliminary evidence suggests these ISL and vortex scaling behaviors both result from mutual interaction with the local large-scale UMZs, possibly through a stretching mechanism. Addi- tional experiments in three dimensions are required to verify the dynamics. The overall findings support the universality of large-scale structures in the outer region and provide promising clues for better understanding scale interaction and energy transfer mechanisms. iii Table of contents List of tables........................................................... vi List of figures .......................................................... vii Nomenclature ..........................................................x 1. Introduction.........................................................1 1.1 What is turbulence? . .2 1.2 What is a boundary layer? . .4 1.3 Coherent structures, eddies, and other terminology . .7 1.4 Research questions . .7 2. Literature review and further background..................................9 2.1 The regions of a turbulent boundary layer and related theory . .9 2.2 A brief history of coherent structure research and related models . 14 3. Atmospheric surface layer measurements using particle image velocimetry ....... 27 3.1 Methodology . 27 3.2 Meteorological conditions . 34 3.3 Measurement validation . 39 3.4 Canonical or not? . 43 4. Detection of coherent structures in the surface layer ......................... 44 4.1 Hairpin-like packet signature . 44 4.2 Uniform momentum zones . 49 4.3 Internal shear layers . 56 4.4 Vortex structures . 58 4.5 Results in the context of Townsend’s attached eddies . 62 5. Uniform momentum zones and the mean velocity profile ..................... 65 5.1 The unanswered question . 65 5.2 Methodology . 66 5.3 Average momentum zone properties and the mean shear . 72 5.4 Momentum zone probability distributions . 75 6. Vortex cores and internal shear layers..................................... 77 6.1 Parameterizing the small scales . 77 6.2 The model vortex and detection algorithm . 79 6.3 Vortex size . 82 6.4 Vortex velocity . 85 6.5 Vortex advection . 88 6.6 Internal shear layer size and advection . 89 iv 6.7 Where are all the Kolmogorov-scaled vortices? . 92 7. Phenomenological interpretation of the results.............................. 94 7.1 The interaction of momentum zones and shear layers . 94 7.2 The Taylor microscale . 98 7.3 A thought on the incremental energy cascade . 100 8. Concluding remarks .................................................. 104 References ............................................................ 106 v List of tables I. Meteorological conditions during the field measurements...................... 34 II. Scaling parameters for the field measurements. ............................. 39 III. Experimental datasets used in the comparison of UMZ properties. ............. 67 IV. Additional parameters for the new wind tunnel experiments. .................. 68 V. Experimental datasets used in the comparison of vortex and shear layer properties.. 78 vi List of figures 1. Sketch of turbulent water by Leonardo da Vinci. ............................1 2. Cartoon of laminar and turbulent flows. ...................................3 3. Cartoon of a boundary layer.............................................5 4. Cartoon of an atmospheric boundary layer during the day and night. ............6 5. Regions of a turbulent boundary layer. .................................... 10 6. Depiction of a double-cone eddy by A. A. Townsend. ........................ 12 7. Cartoon comparing a smooth- and rough-wall boundary layer. ................. 13 8. Depiction of Theodorsen’s horseshoe vortex................................ 15 9. Photograph of low-speed streaks by Kline and co-authors. .................... 15 10. Conceptual bursting model by Kline and co-authors. ........................ 15 11. Attached eddy structural model of Perry & Chong. ......................... 16 12. Representative Λ-vortex packet by Woodcock & Marusic..................... 17 13. Contours of instantaneous and average vortex structures from Dennis & Kunkel... 18 14. The rolls associated with streamwise momentum streaks from Jimenez.´ ......... 20 15. Quadrant classification of Reynolds shear stress statistics..................... 21 16. Uniform momentum zones (UMZs) in a boundary layer. ..................... 22 17. Clustering of strain and vorticity in isotropic turbulence from Ishihara et al. ..... 26 18. Aerial satellite image of the Eolos field site................................ 28 19.