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Surface wave effects on energy transfer in overlying turbulent flow

Published online by Cambridge University Press:  22 April 2020

Li-Hao Wang
Affiliation:
Applied Mechanics Laboratory, Department of Engineering Mechanics, Tsinghua University, Beijing100084, China
Wu-Yang Zhang
Affiliation:
Applied Mechanics Laboratory, Department of Engineering Mechanics, Tsinghua University, Beijing100084, China
Xuanting Hao
Affiliation:
Department of Mechanical Engineering and Saint Anthony Falls Laboratory, University of Minnesota, Minneapolis, MN 55455, USA
Wei-Xi Huang*
Affiliation:
Applied Mechanics Laboratory, Department of Engineering Mechanics, Tsinghua University, Beijing100084, China
Lian Shen
Affiliation:
Department of Mechanical Engineering and Saint Anthony Falls Laboratory, University of Minnesota, Minneapolis, MN 55455, USA
Chun-Xiao Xu
Affiliation:
Applied Mechanics Laboratory, Department of Engineering Mechanics, Tsinghua University, Beijing100084, China
Zhaoshun Zhang
Affiliation:
Applied Mechanics Laboratory, Department of Engineering Mechanics, Tsinghua University, Beijing100084, China
*
Email address for correspondence: hwx@tsinghua.edu.cn

Abstract

Phase-resolved wave simulation and direct numerical simulation of turbulence are performed to investigate the surface wave effects on the energy transfer in overlying turbulent flow. The JONSWAP spectrum is used to initialize a broadband wave field. The nonlinear wave field is simulated using a high-order spectral method, and the resultant wave surface provides the bottom boundary conditions for direct numerical simulation of the overlying turbulent flow. Two wave ages of $c_{p}/u_{\ast }=2$ and 25 are considered, corresponding to slow and fast wave fields, respectively, where $c_{p}$ denotes the celerity of the peak wave and $u_{\ast }$ denotes the friction velocity. The energy transfer of turbulent motions in the presence of surface waves is investigated through the spectral analysis of the two-point correlation transport equation. It is found that the production term has an extra peak at the dominant wavelength scale in the vicinity of the surface, and the energy transported to the surface via viscous and spatial turbulent transport is enhanced in the region of $y^{+}<10$. The presence of surface waves results in an inverse turbulent energy cascade in the near-surface region, where small-scale wave-related motions transfer energy back to the dominant wavelength scale. Pressure-related terms reflecting the spatial and inter-component energy transfer are strongly dependent on the wave age. Furthermore, triadic interaction analysis reveals that the energy influx at the dominant wavelength scale is due to the contribution of the neighbouring streamwise turbulent motions, and those at the harmonic wavelength scales contribute the most.

Type
JFM Papers
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

Belcher, S. E. & Hunt, J. C. R. 1993 Turbulent shear flow over slowly moving waves. J. Fluid Mech. 251, 109148.CrossRefGoogle Scholar
Black, P. G., D’Asaro, E. A., Drennan, W. M., French, J. R., Niiler, P. P., Sanford, T. B., Terrill, E. J., Walsh, E. J. & Zhang, J. A. 2007 Air–sea exchange in hurricanes: synthesis of observations from the coupled boundary layer air–sea transfer experiment. Bull. Am. Meteorol. Soc. 88, 357374.CrossRefGoogle Scholar
Breivik, Ø., Mogensen, K., Bidlot, J. R., Balmaseda, M. A. & Janssen, P. A. 2015 Surface wave effects in the NEMO ocean model: forced and coupled experiments. J. Geophys. Res. 120, 29732992.Google Scholar
Buckley, M. P. & Veron, F. 2016 Structure of the airflow above surface waves. J. Phys. Oceanogr. 46, 13771397.CrossRefGoogle Scholar
Buckley, M. P. & Veron, F. 2019 The turbulent airflow over wind generated surface waves. Eur. J. Mech. (B/Fluids) 73, 132143.CrossRefGoogle Scholar
Chen, S. S., Zhao, W., Donelan, M. A. & Tolman, H. L. 2013 Directional wind–wave coupling in fully coupled atmosphere–wave–ocean models: results from CBLAST-Hurricane. J. Atmos. Sci. 70, 31983215.CrossRefGoogle Scholar
Cho, M., Hwang, Y. & Choi, H. 2018 Scale interactions and spectral energy transfer in turbulent channel flow. J. Fluid Mech. 854, 474504.CrossRefGoogle Scholar
Choi, H., Moin, P. & Kim, J. 1993 Direct numerical simulation of turbulent flow over riblets. J. Fluid Mech. 255, 503539.CrossRefGoogle Scholar
Cimarelli, A., De Angelis, E. & Casciola, C. M. 2013 Paths of energy in turbulent channel flows. J. Fluid Mech. 715, 436451.CrossRefGoogle Scholar
Cimarelli, A., De Angelis, E., Jiménez, J. & Casciola, C. M. 2016 Cascades and wall-normal fluxes in turbulent channel flows. J. Fluid Mech. 796, 417436.CrossRefGoogle Scholar
Cohen, J. E. & Belcher, S. E. 1999 Turbulent shear flow over fast-moving waves. J. Fluid Mech. 386, 345371.CrossRefGoogle Scholar
Domaradzki, J. A., Liu, W., Härtel, C. & Kleiser, L. 1994 Energy transfer in numerically simulated wall-bounded turbulent flows. Phys. Fluids 6, 15831599.CrossRefGoogle Scholar
Dommermuth, D. G. & Yue, D. K. P. 1987 A high-order spectral method for the study of nonlinear gravity waves. J. Fluid Mech. 184, 267288.CrossRefGoogle Scholar
Druzhinin, O. A., Troitskaya, Y. I. & Zilitinkevich, S. S. 2012 Direct numerical simulation of a turbulent wind over a wavy water surface. J. Geophys. Res. 117, C00J05.CrossRefGoogle Scholar
Dubrulle, B. 2019 Beyond Kolmogorov cascades. J. Fluid Mech. 867, P1.CrossRefGoogle Scholar
Edson, J., Crawford, T., Crescenti, J., Farrar, T., Frew, N., Gerbi, G., Helmis, C., Hristov, T., Khelif, D., Jessup, A. et al. 2007 The coupled boundary layers and air–sea transfer experiment in low winds. Bull. Am. Meteorol. Soc. 88, 341356.CrossRefGoogle Scholar
Ge, M. W., Xu, C. X. & Cui, G. X. 2010 Direct numerical simulation of flow in channel with time-dependent wall geometry. Appl. Math. Mech. 31, 97108.CrossRefGoogle Scholar
Grare, L., Lenain, L. & Melville, W. K. 2013 Wave-coherent airflow and critical layers over ocean waves. J. Phys. Oceanogr. 43, 21562172.CrossRefGoogle Scholar
Hamilton, J. M., Kim, J. & Waleffe, F. 1995 Regeneration mechanisms of near-wall turbulence structures. J. Fluid Mech. 287, 317348.CrossRefGoogle Scholar
Hao, X. & Shen, L. 2019 Wind–wave coupling study using LES of wind and phase-resolved simulation of nonlinear waves. J. Fluid Mech. 874, 391425.CrossRefGoogle Scholar
Hara, T. & Sullivan, P. P. 2015 Wave boundary layer turbulence over surface waves in a strongly forced condition. J. Phys. Oceanogr. 45, 868883.CrossRefGoogle Scholar
Hasselmann, K., Barnett, T. P., Bouws, E., Carlson, H., Cartwright, D. E., Enke, K., Ewing, J. A., Gienapp, H., Hasselmann, D. E., Kruseman, P. et al. 1973 Measurements of wind-wave growth and swell decay during the joint north sea wave project (JONSWAP). Erg. Deutsch. Hydrogr. Z. 12 (A8), 195. Deutches Hydrographisches Institut.Google Scholar
Hill, R. J. 2002 Exact second-order structure-function relationships. J. Fluid Mech. 468, 317326.CrossRefGoogle Scholar
Hristov, T. S., Miller, S. D. & Friehe, C. A. 2003 Dynamical coupling of wind and ocean waves through wave-induced air flow. Nature 422, 5558.CrossRefGoogle ScholarPubMed
Husain, N. T., Hara, T., Buckley, M. P., Yousefi, K., Veron, F. & Sullivan, P. P. 2019 Boundary layer turbulence over surface waves in a strongly forced condition: LES and observation. J. Phys. Oceanogr. 49, 19972015.CrossRefGoogle Scholar
Hussain, A. K. M. F. & Reynolds, W. C. 1970 The mechanics of an organized wave in turbulent shear flow. J. Fluid Mech. 41, 241258.CrossRefGoogle Scholar
Jiménez, J. & Pinelli, A. 1999 The autonomous cycle of near-wall turbulence. J. Fluid Mech. 389, 335359.CrossRefGoogle Scholar
Kang, S. & Choi, H. 2000 Active wall motions for skin-friction drag reduction. Phys. Fluids 12, 3301.CrossRefGoogle Scholar
Kihara, N., Hanazaki, H., Mizuya, T. & Ueda, H. 2007 Relationship between airflow at the critical height and momentum transfer to the traveling waves. Phys. Fluids 19, 015102.CrossRefGoogle Scholar
Kolmogorov, A. N. 1941a The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers. Dokl. Akad. Nauk SSSR 30, 913.Google Scholar
Kolmogorov, A. N. 1941b Dissipation of energy in the locally isotropic turbulence. Dokl. Akad. Nauk SSSR 32, 1618.Google Scholar
Kraichnan, R. 1971 Inertial-range transfer in two-and three-dimensional turbulence. J. Fluid Mech. 47, 525535.CrossRefGoogle Scholar
Kuhn, S., Wagner, C. & von Rohr, P. R. 2007 Influence of wavy surfaces on coherent structures in a turbulent flow. Exp. Fluids 43, 251259.CrossRefGoogle Scholar
Lee, M. & Moser, R. D. 2015 Spectral analysis on Reynolds stress transport equation in high Re wall-bounded turbulence. In 9th International Symposium on Turbulence and Shear Flow Phenomena, Melbourne, Australia, 4A–3. TSFP9.Google Scholar
Lee, M. & Moser, R. D. 2019 Spectral analysis of the budget equation in turbulent channel flows at high Reynolds number. J. Fluid Mech. 860, 886938.CrossRefGoogle Scholar
Liu, Y., Yang, D., Guo, X. & Shen, L. 2010 Numerical study of pressure forcing of wind on dynamically evolving water waves. Phys. Fluids 22, 041704.CrossRefGoogle Scholar
Lumley, J. L. 1964 Spectral energy budget in wall turbulence. Phys. Fluids 7, 190196.CrossRefGoogle Scholar
Marati, N., Casciola, C. M. & Piva, R. 2004 Energy cascade and spatial fluxes in wall turbulence. J. Fluid Mech. 521, 191215.CrossRefGoogle Scholar
Marusic, I., Mathis, R. & Hutchins, N. 2010 High Reynolds number effects in wall turbulence. Intl J. Heat Fluid Flow 31, 418428.CrossRefGoogle Scholar
Mastenbroek, C., Makin, V. K., Garat, M. H. & Giovanangeli, J. P. 1996 Experimental evidence of the rapid distortion of turbulence in the air flow over water waves. J. Fluid Mech. 318, 273302.CrossRefGoogle Scholar
Mei, C. C., Stiassnie, M. & Yue, D. K. P. 2005 Theory and Applications of Ocean Surface Waves: Nonlinear Aspects. World Scientific.Google Scholar
Meneveau, C. & Katz, J. 2000 Scale-invariance and turbulence models for large-eddy simulation. Annu. Rev. Fluid Mech. 32, 132.CrossRefGoogle Scholar
Miles, J. W. 1957 On the generation of surface waves by shear flows. J. Fluid Mech. 3, 185204.CrossRefGoogle Scholar
Mizuno, Y. 2016 Spectra of energy transport in turbulent channel flows for moderate Reynolds numbers. J. Fluid Mech. 805, 171187.CrossRefGoogle Scholar
Phillips, O. M. 1957 On the generation of waves by turbulent wind. J. Fluid Mech. 2, 417445.CrossRefGoogle Scholar
Plant, W. J. 1982 A relationship between wind stress and wave slope. J. Geophys. Res. 87, 19611967.CrossRefGoogle Scholar
Richardson, L. F. 1922 Weather Prediction by Numerical Process. Cambridge University Press.Google Scholar
Rutgersson, A. & Sullivan, P. P. 2005 The effect of idealized water waves on the turbulence structure and kinetic energy budgets in the overlying airflow. Dyn. Atmos. Ocean 38, 147171.CrossRefGoogle Scholar
Shen, L., Zhang, X., Yue, D. K. P. & Triantafyllou, M. S. 2003 Turbulent flow over a flexible wall undergoing a streamwise travelling wave motion. J. Fluid Mech. 484, 197221.CrossRefGoogle Scholar
Siddiqui, M. K. & Loewen, M. R. 2007 Characteristics of the wind drift layer and microscale breaking waves. J. Fluid Mech. 573, 417456.CrossRefGoogle Scholar
Smits, A. J., McKeon, B. J. & Marusic, I. 2011 High-Reynolds number wall turbulence. Annu. Rev. Fluid Mech. 43, 353375.CrossRefGoogle Scholar
Sullivan, P. P. & McWilliams, J. C. 2010 Dynamics of winds and currents coupled to surface waves. Annu. Rev. Fluid Mech. 42, 1942.CrossRefGoogle Scholar
Sullivan, P. P., McWilliams, J. C. & Moeng, C. H. 2000 Simulation of turbulent flow over idealized water waves. J. Fluid Mech. 404, 4785.CrossRefGoogle Scholar
Sullivan, P. P., McWilliams, J. C. & Patton, E. G. 2014 Large-eddy simulation of marine atmospheric boundary layers above a spectrum of moving waves. J. Atmos. Sci. 71, 40014027.CrossRefGoogle Scholar
Tanaka, M. 2001 A method of studying nonlinear random field of surface gravity waves by direct numerical simulation. Fluid Dyn. Res. 28, 4160.CrossRefGoogle Scholar
Thais, L. & Magnaudet, J. 1996 Turbulent structure beneath surface gravity waves sheared by the wind. J. Fluid Mech. 328, 313344.CrossRefGoogle Scholar
Vassilicos, J. C. 2015 Dissipation in turbulent flows. Annu. Rev. Fluid Mech. 47, 95114.CrossRefGoogle Scholar
Xiao, W., Liu, Y., Wu, G. & Yue, D. K. P. 2013 Rogue wave occurrence and dynamics by direct simulations of nonlinear wave-field evolution. J. Fluid Mech. 720, 357392.CrossRefGoogle Scholar
Yang, D., Meneveau, C. & Shen, L. 2013 Dynamic modelling of sea-surface roughness for large-eddy simulation of wind over ocean wavefield. J. Fluid Mech. 726, 6299.CrossRefGoogle Scholar
Yang, D., Meneveau, C. & Shen, L. 2014 Large-eddy simulation of offshore wind farm. Phys. Fluids 26, 025101.CrossRefGoogle Scholar
Yang, D. & Shen, L. 2009 Characteristics of coherent vortical structures in turbulent flows over progressive surface waves. Phys. Fluids 21, 125106.CrossRefGoogle Scholar
Yang, D. & Shen, L. 2010 Direct-simulation-based study of turbulent flow over various waving boundaries. J. Fluid Mech. 650, 131180.CrossRefGoogle Scholar
Yang, D. & Shen, L. 2011 Simulation of viscous flows with undulatory boundaries: Part II. Coupling with other solvers for two-fluid computations. J. Comput. Phys. 230, 55105531.CrossRefGoogle Scholar
Yang, D. & Shen, L. 2017 Direct numerical simulation of scalar transport in turbulent flows over progressive surface waves. J. Fluid Mech. 819, 58103.CrossRefGoogle Scholar
Zhang, W. Y., Huang, W. X. & Xu, C. X. 2019 Very large-scale motions in turbulent flows over streamwise traveling wavy boundaries. Phys. Rev. Fluids 4, 054601.CrossRefGoogle Scholar
Zhou, J., Adrian, R. J., Balachandar, S. & Kendall, T. M. 1999 Mechanisms for generating coherent packets of hairpin vortices in channel flow. J. Fluid Mech. 387, 353396.CrossRefGoogle Scholar