Hostname: page-component-669899f699-b58lm Total loading time: 0 Render date: 2025-04-25T06:48:19.604Z Has data issue: false hasContentIssue false

Dynamics of turbulence production by attenuating interfacial gravity waves observed in air–water coupled wave-resolving simulation

Published online by Cambridge University Press:  21 November 2024

Yasushi Fujiwara*
Affiliation:
Graduate School of Maritime Sciences, Kobe University, Kobe, 6580022, Japan
*
Email address for correspondence: [email protected]

Abstract

Even without breaking or wind influence, ocean surface waves are observed to produce turbulence in the water, possibly influencing ocean surface dynamics and air–sea interactions. Based on the water-side free-surface simulations, recent studies suggest that such turbulence is produced through the interaction between the waves and the near-surface Eulerian current associated with the viscous attenuation of waves. To clarify the dynamical role of the air–water interface in the turbulence production, the attenuating interfacial gravity waves were simulated directly using a newly developed two-phase wave-resolving numerical model. The air–water coupling enhanced the wave energy dissipation through the formation of a strong shear at the air-side viscous boundary layer. This led to an enhancement of the wave-to-current momentum transfer and the formation of the down-wave Eulerian mean sheared current, which is favourable for the CL2 instability responsible for the production of Langmuir circulations. As a result, the water-side turbulence grew stronger compared with the corresponding free surface (water-only) wave-resolving simulation. The evolution of the wave-averaged field was well reproduced with the Craik–Leibovich equation with the upper boundary condition provided with the virtual wave stress based on linear theory. The wave energy dissipation by air–water coupling plays a significant role in the quantitative understanding of the wave-induced turbulence at the laboratory and field scales.

Type
JFM Papers
Copyright
© The Author(s), 2024. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Ardhuin, F., et al. 2010 Semiempirical dissipation source functions for ocean waves. Part I. Definition, calibration, and validation. J. Phys. Oceanogr. 40 (9), 19171941.CrossRefGoogle Scholar
Babanin, A.V. 2006 On a wave-induced turbulence and a wave-mixed upper ocean layer. Geophys. Res. Lett. 33, L20605.CrossRefGoogle Scholar
Babanin, A.V. & Haus, B.K. 2009 On the existence of water turbulence induced by nonbreaking surface waves. J. Phys. Oceanogr. 39 (10), 26752679.CrossRefGoogle Scholar
Belcher, S.E., et al. 2012 A global perspective on Langmuir turbulence in the ocean surface boundary layer. Geophys. Res. Lett. 39, L18605.CrossRefGoogle Scholar
Cao, T. & Shen, L. 2021 A numerical and theoretical study of wind over fast-propagating water waves. J. Fluid Mech. 919, A38.CrossRefGoogle Scholar
Colagrossi, A. & Landrini, M. 2003 Numerical simulation of interfacial flows by smoothed particle hydrodynamics. J. Comput. Phys. 191 (2), 448475.CrossRefGoogle Scholar
Craik, A.D.D. & Leibovich, S. 1976 A rational model for Langmuir circulations. J. Fluid Mech. 73 (03), 401426.CrossRefGoogle Scholar
D'Asaro, E.A. 2014 Turbulence in the upper-ocean mixed layer. Ann. Rev. Mar. Sci. 6, 101115.CrossRefGoogle ScholarPubMed
Dai, D., Qiao, F., Sulisz, W., Han, L. & Babanin, A. 2010 An experiment on the nonbreaking surface-wave-induced vertical mixing. J. Phys. Oceanogr. 40 (9), 21802188.CrossRefGoogle Scholar
Deike, L., Popinet, S. & Melville, W.K. 2015 Capillary effects on wave breaking. J. Fluid Mech. 769, 541569.CrossRefGoogle Scholar
Dore, B.D. 1978 Some effects of the air–water interface on gravity waves. Geophys. Astrophys. Fluid Dyn. 10 (1), 215230.CrossRefGoogle Scholar
Fenton, J.D. 1985 A fifth-order Stokes theory for steady waves. ASCE J. Waterway Port Coastal Ocean Engng 111 (2), 216234.CrossRefGoogle Scholar
Fujiwara, Y. & Yoshikawa, Y. 2020 Mutual interaction between surface waves and Langmuir circulations observed in wave-resolving numerical simulations. J. Phys. Oceanogr. 50 (8), 23232339.CrossRefGoogle Scholar
Fujiwara, Y., Yoshikawa, Y. & Matsumura, Y. 2018 A wave-resolving simulation of Langmuir circulations with a nonhydrostatic free-surface model: comparison with Craik–Leibovich theory and an alternative Eulerian view of the driving mechanism. J. Phys. Oceanogr. 48 (8), 16911708.CrossRefGoogle Scholar
Fujiwara, Y., Yoshikawa, Y. & Matsumura, Y. 2020 Wave-resolving simulations of viscous wave attenuation effects on Langmuir circulation. Ocean Model. 154, 101679.CrossRefGoogle Scholar
Fulgosi, M., Lakehal, D., Banerjee, S. & De Angelis, V. 2003 Direct numerical simulation of turbulence in a sheared air–water flow with a deformable interface. J. Fluid Mech. 482, 319345.CrossRefGoogle Scholar
Guo, X. & Shen, L. 2013 Numerical study of the effect of surface waves on turbulence underneath. Part 1. Mean flow and turbulence vorticity. J. Fluid Mech. 733, 558587.CrossRefGoogle Scholar
Guo, X. & Shen, L. 2014 Numerical study of the effect of surface wave on turbulence underneath. Part 2. Eulerian and Lagrangian properties of turbulence kinetic energy. J. Fluid Mech. 744, 250272.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
Harlow, F.H. & Welch, J.E. 1965 Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface. Phys. Fluids 8 (12), 2182.CrossRefGoogle Scholar
Imamura, H., Yoshikawa, Y. & Fujiwara, Y. n.d. Direct numerical simulations of the nonbreaking surface-wave-induced turbulence. Ocean Dyn. (submitted).Google Scholar
Komori, S., Kurose, R., Iwano, K., Ukai, T. & Suzuki, N. 2010 Direct numerical simulation of wind-driven turbulence and scalar transfer at sheared gas–liquid interfaces. J. Turbul. 11, N32.CrossRefGoogle Scholar
Lamb, H. 1932 Hydrodynamics. The University Press.Google Scholar
Langmuir, I. 1938 Surface motion of water induced by wind. Science 87 (2250), 119123.CrossRefGoogle ScholarPubMed
Leibovich, S. 1983 The form and dynamics of Langmuir circulations. Annu Rev. Fluid Mech. 15 (1), 391427.CrossRefGoogle Scholar
Li, Q., et al. 2019 Comparing ocean surface boundary vertical mixing schemes including Langmuir turbulence. J. Adv. Model. Earth Syst. 11 (11), 35453592.CrossRefGoogle Scholar
Li, Y. & Chabchoub, A. 2024 How currents trigger extreme sea waves, the roles of stokes drift, Eulerian return flow, and a background flow in the open ocean. Geophys. Res. Lett. 51 (6), e2023GL107381.CrossRefGoogle Scholar
Li, T. & Shen, L. 2022 The principal stage in wind–wave generation. J. Fluid Mech. 934, A41.CrossRefGoogle Scholar
Lin, M.-Y., Moeng, C.-H., Tsai, W.-T., Sullivan, P.P. & Belcher, S.E. 2008 Direct numerical simulation of wind–wave generation processes. J. Fluid Mech. 616, 130.CrossRefGoogle Scholar
Lombardi, P., De Angelis, V. & Banerjee, S. 1996 Direct numerical simulation of near-interface turbulence in coupled gas–liquid flow. Phys. Fluids 8 (6), 16431665.CrossRefGoogle Scholar
Longuet-Higgins, M.S. 1953 Mass transport in water waves. Phil. Trans. R. Soc. Lond. A 245 (903), 535581.Google Scholar
Longuet-Higgins, M.S. 1969 A nonlinear mechanism for the generation of sea waves. Proc. R. Soc. Lond. A 311 (1506), 371389.Google Scholar
Miles, J.W. 1957 On the generation of surface waves by shear flows. J. Fluid Mech. 3 (2), 185204.CrossRefGoogle Scholar
Miles, J.W. 1959 On the generation of surface waves by shear flows. Part 2. J. Fluid Mech. 6 (4), 568582.CrossRefGoogle Scholar
Phillips, O.M. 1966 The Dynamics of the Upper Ocean. Cambridge University Press.Google Scholar
Pleskachevsky, A., Dobrynin, M., Babanin, A.V., Günther, H. & Stanev, E. 2011 Turbulent mixing due to surface waves indicated by remote sensing of suspended particulate matter and its implementation into coupled modeling of waves, turbulence, and circulation. J. Phys. Oceanogr. 41 (4), 708724.CrossRefGoogle Scholar
Popinet, S. 2003 Gerris: a tree-based adaptive solver for the incompressible Euler equations in complex geometries. J. Comput. Phys. 190 (2), 572600.CrossRefGoogle Scholar
Savelyev, I.B., Maxeiner, E. & Chalikov, D. 2012 Turbulence production by nonbreaking waves: laboratory and numerical simulations. J. Geophys. Res.: Oceans 117, C00J13.CrossRefGoogle Scholar
Stokes, G.G. 1847 On the theory of oscillatory waves. Trans. Camb. Phil. Soc. 8, 441455.Google Scholar
Sullivan, P.P., Edson, J.B., Hristov, T. & McWilliams, J.C. 2008 Large-eddy simulations and observations of atmospheric marine boundary layers above nonequilibrium surface waves. J. Atmos. Sci. 65 (4), 12251245.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
Sussman, M., Almgren, A.S., Bell, J.B., Colella, P., Howell, L.H. & Welcome, M.L. 1999 An adaptive level set approach for incompressible two-phase flows. J. Comput. Phys. 148 (1), 81124.CrossRefGoogle Scholar
Teixeira, M.A.C. & Belcher, S.E. 2002 On the distortion of turbulence by a progressive surface wave. J. Fluid Mech. 458, 229267.CrossRefGoogle Scholar
Tsai, W.-T., Chen, S.-M. & Lu, G.-H. 2015 Numerical evidence of turbulence generated by nonbreaking surface waves. J. Phys. Oceanogr. 45 (1), 174180.CrossRefGoogle Scholar
Tsai, W.-T., Chen, S.-M., Lu, G.-H. & Garbe, C.S. 2013 Characteristics of interfacial signatures on a wind-driven gravity-capillary wave. J. Geophys. Res.: Oceans 118 (4), 17151735.CrossRefGoogle Scholar
Tsai, W.-T. & Hung, L.-P. 2007 Three-dimensional modeling of small-scale processes in the upper boundary layer bounded by a dynamic ocean surface. J. Geophys. Res.: Oceans 112, C02019.CrossRefGoogle Scholar
Tsai, W.-T. & Lu, G.-H. 2023 A numerical study on Langmuir circulations and coherent vortical structures beneath surface waves. J. Fluid Mech. 969, A30.CrossRefGoogle Scholar
Tsai, W.-T., Lu, G.-H., Chen, J.-R., Dai, A. & Phillips, W.R.C. 2017 On the formation of coherent vortices beneath nonbreaking free-propagating surface waves. J. Phys. Oceanogr. 47 (3), 533543.CrossRefGoogle Scholar
Tsuji, Y. & Nagata, Y. 1973 Stokes’ expansion of internal deep water waves to the fifth order. J. Oceanogr. Soc. Japan 29, 6169.CrossRefGoogle Scholar
Veron, F. & Melville, W.K. 2001 Experiments on the stability and transition of wind-driven water surfaces. J. Fluid Mech. 446, 2565.CrossRefGoogle Scholar
Villas Bôas, A.B., et al. 2019 Integrated observations of global surface winds, currents, and waves: requirements and challenges for the next decade. Front. Mar. Sci. 6, 425.CrossRefGoogle Scholar
Wang, P. & Özgökmen, T.M. 2018 Langmuir circulation with explicit surface waves from moving-mesh modeling. Geophys. Res. Lett. 45 (1), 216226.CrossRefGoogle Scholar
Wu, J. & Deike, L. 2021 Wind wave growth in the viscous regime. Phys. Rev. Fluids 6 (9), 094801.CrossRefGoogle Scholar
Wu, L., Rutgersson, A. & Sahlée, E. 2015 Upper-ocean mixing due to surface gravity waves. J. Geophys. Res.: Oceans 120 (12), 82108228.CrossRefGoogle Scholar
Xuan, A., Deng, B.-Q. & Shen, L. 2019 Study of wave effect on vorticity in Langmuir turbulence using wave-phase-resolved large-eddy simulation. J. Fluid Mech. 875, 173224.CrossRefGoogle Scholar
Xuan, A. & Shen, L. 2019 A conservative scheme for simulation of free-surface turbulent and wave flows. J. Comput. Phys. 378, 1843.CrossRefGoogle Scholar
Yang, D. & Shen, L. 2011 a Simulation of viscous flows with undulatory boundaries. Part I. Basic solver. J. Comput. Phys. 230 (14), 54885509.CrossRefGoogle Scholar
Yang, D. & Shen, L. 2011 b Simulation of viscous flows with undulatory boundaries. Part II. Coupling with other solvers for two-fluid computations. J. Comput. Phys. 230 (14), 55105531.CrossRefGoogle Scholar
Zonta, F., Onorato, M. & Soldati, A. 2016 Decay of gravity-capillary waves in air/water sheared turbulence. Intl J. Heat Fluid Flow 61, 137144.CrossRefGoogle Scholar
Zonta, F., Soldati, A. & Onorato, M. 2015 Growth and spectra of gravity–capillary waves in countercurrent air/water turbulent flow. J. Fluid Mech. 777, 245259.CrossRefGoogle Scholar