Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-11T09:36:34.623Z Has data issue: false hasContentIssue false
  • English
  • Français

Study of wave effect on vorticity in Langmuir turbulence using wave-phase-resolved large-eddy simulation

Published online by Cambridge University Press:  18 July 2019

Anqing Xuan Open the ORCID record for Anqing Xuan [Opens in a new window] ,
Bing-Qing Deng Open the ORCID record for Bing-Qing Deng [Opens in a new window]  and
Lian Shen Open the ORCID record for Lian Shen [Opens in a new window]
Anqing Xuan
Affiliation:
Department of Mechanical Engineering and Saint Anthony Falls Laboratory, University of Minnesota, Minneapolis, MN 55455, USA
Bing-Qing Deng
Affiliation:
Department of Mechanical Engineering and Saint Anthony Falls Laboratory, University of Minnesota, Minneapolis, MN 55455, USA
Lian Shen*
Affiliation:
Department of Mechanical Engineering and Saint Anthony Falls Laboratory, University of Minnesota, Minneapolis, MN 55455, USA
*
†Email address for correspondence: shen@umn.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

The effects of a water surface wave on the vorticity in the turbulence underneath are studied for Langmuir turbulence using wave-phase-resolved large-eddy simulation. The simulations are performed on a dynamically evolving wave-surface-fitted grid such that the phase-resolved wave motions and their effects on the turbulence are explicitly captured. This study focuses on the vorticity structures and dynamics in Langmuir turbulence driven by a steady and co-aligned progressive wave and surface shear stress. For the first time, the detailed vorticity dynamics of the wave–turbulence interaction in Langmuir turbulence in a wave-phase-resolved frame is revealed. The wave-phase-resolved simulation provides detailed descriptions of many characteristic features of Langmuir turbulence, such as elongated quasi-streamwise vortices. The simulation also reveals the variation of the strength and the inclination angles of the vortices with the wave phase. The variation is found to be caused by the periodic stretching and tilting of the wave orbital straining motions. The cumulative effect of the wave on the wave-phase-averaged vorticity is analysed using the Lagrangian average. It is discovered that, in addition to the tilting effect induced by the Lagrangian mean shear gradient of the wave, the phase correlation between the vorticity fluctuations and the wave orbital straining is also important to the cumulative vorticity evolution. Both the fluctuation correlation effect and the mean tilting effect are found to amplify the streamwise vorticity. On the other hand, for the vertical vorticity, the fluctuation correlation effect cancels the mean tilting effect, and the net change of the vertical vorticity by the wave straining is negligible. As a result, the wave straining enhances only the streamwise vorticity and cumulatively tilts vertical vortices towards the streamwise direction. The above processes are further quantified analytically. The role of the fluctuation correlation effect in the wave-phase-averaged vorticity dynamics provides a deeper understanding of the physical processes underlying the wave–turbulence interaction in Langmuir turbulence.

JFM classification

Geophysical and Geological Flows: Ocean processes
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 875 , 25 September 2019 , pp. 173 - 224
Copyright
© 2019 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.)

References

Adrian, R. J. 1994 Stochastic estimation of conditional structure: a review. Appl. Sci. Res. 53 (3-4), 291–303.Google Scholar
Adrian, R. J. & Moin, P. 1988 Stochastic estimation of organized turbulent structure: Homogeneous shear flow. J. Fluid Mech. 190, 531–559.Google Scholar
Andrews, D. G. & Mcintyre, M. E. 1978 An exact theory of nonlinear waves on a Lagrangian-mean flow. J. Fluid Mech. 89 (04), 609–646.Google Scholar
Ardhuin, F. & Jenkins, A. D. 2006 On the interaction of surface waves and upper ocean turbulence. J. Phys. Oceanogr. 36 (3), 551–557.Google Scholar
Ardhuin, F., Rascle, N. & Belibassakis, K. 2008 Explicit wave-averaged primitive equations using a generalized Lagrangian mean. Ocean Model. 20 (1), 35–60.Google Scholar
Belcher, S. E., Grant, A. L. M., Hanley, K. E., Fox-Kemper, B., Van Roekel, L., Sullivan, P. P., Large, W. G., Brown, A., Hines, A., Calvert, D. et al. 2012 A global perspective on Langmuir turbulence in the ocean surface boundary layer. Geophys. Res. Lett. 39 (18), L18605.Google Scholar
Bhaskaran, R. & Leibovich, S. 2002 Eulerian and Lagrangian Langmuir circulation patterns. Phys. Fluids 14 (7), 2557–2571.Google Scholar
Bou-Zeid, E., Meneveau, C. & Parlange, M. 2005 A scale-dependent Lagrangian dynamic model for large eddy simulation of complex turbulent flows. Phys. Fluids 17 (2), 025105.Google Scholar
Chapman, D. R. 1979 Computational aerodynamics development and outlook. AIAA J. 17 (12), 1293–1313.Google Scholar
Chen, B., Yang, D., Meneveau, C. & Chamecki, M. 2016 Effects of swell on transport and dispersion of oil plumes within the ocean mixed layer. J. Geophys. Res.-Oceans 121 (5), 3564–3578.Google Scholar
Choi, H. & Moin, P. 2012 Grid-point requirements for large eddy simulation: Chapman’s estimates revisited. Phys. Fluids 24 (1), 011702.Google Scholar
Christensen, K. T. & Adrian, R. J. 2001 Statistical evidence of hairpin vortex packets in wall turbulence. J. Fluid Mech. 431, 433–443.Google Scholar
Craik, A. D. D. 1977 The generation of Langmuir circulations by an instability mechanism. J. Fluid Mech. 81 (02), 209–223.Google Scholar
Craik, A. D. D. 1982 Wave-induced longitudinal-vortex instability in shear flows. J. Fluid Mech. 125, 37–52.Google Scholar
Craik, A. D. D. & Leibovich, S. 1976 A rational model for Langmuir circulations. J. Fluid Mech. 73 (03), 401–426.Google Scholar
D’Asaro, E. A. 2014 Turbulence in the upper-ocean mixed layer. Annu. Rev. Mar. Sci. 6, 101–115.Google Scholar
Deng, B.-Q., Yang, Z., Xuan, A. & Shen, L. 2019 Influence of Langmuir circulations on turbulence in the bottom boundary layer of shallow water. J. Fluid Mech. 861, 275–308.Google Scholar
Dimas, A. A. & Fialkowski, L. T. 2000 Large-wave simulation (LWS) of free-surface flows developing weak spilling breaking waves. J. Comput. Phys. 159 (2), 172–196.Google Scholar
Fan, Y. & Griffies, S. M. 2014 Impacts of parameterized Langmuir turbulence and nonbreaking wave mixing in global climate simulations. J. Clim. 27 (12), 4752–4775.Google Scholar
Farmer, D. & Li, M. 1995 Patterns of bubble clouds organized by Langmuir circulation. J. Phys. Oceanogr. 25 (6), 1426–1440.Google Scholar
Fenton, J. D. 1985 A fifth-order Stokes theory for steady waves. J. Waterways Port Coast. Ocean Div. ASCE 111 (2), 216–234.Google 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), 1691–1708.Google Scholar
Ganapathisubramani, B., Longmire, E. K. & Marusic, I. 2003 Characteristics of vortex packets in turbulent boundary layers. J. Fluid Mech. 478, 35–46.Google Scholar
Germano, M., Piomelli, U., Moin, P. & Cabot, W. H. 1991 A dynamic subgrid-scale eddy viscosity model. Phys. Fluids 3 (7), 1760–1765.Google Scholar
Gnanadesikan, A. & Weller, R. A. 1995 Structure and instability of the Ekman spiral in the presence of surface gravity waves. J. Phys. Oceanogr. 25 (12), 3148–3171.Google Scholar
Grant, A. L. M. & Belcher, S. E. 2009 Characteristics of Langmuir turbulence in the ocean mixed layer. J. Phys. Oceanogr. 39 (8), 1871–1887.Google Scholar
Guo, X. & Shen, L. 2009 On the generation and maintenance of waves and turbulence in simulations of free-surface turbulence. Comput. Phys. 228 (19), 7313–7332.Google 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, 558–587.Google 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, 250–272.Google Scholar
Gutiérrez, P. & Aumaître, S. 2016 Surface waves propagating on a turbulent flow. Phys. Fluids 28 (2), 025107.Google Scholar
Harcourt, R. R. & D’Asaro, E. A. 2008 Large-eddy simulation of Langmuir turbulence in pure wind seas. J. Phys. Oceanogr. 38 (7), 1542–1562.Google Scholar
Hodges, B. R. & Street, R. L. 1999 On simulation of turbulent nonlinear free-surface flows. Comput. Phys. 151 (2), 425–457.Google Scholar
Jeong, J. & Hussain, F. 1995 On the identification of a vortex. J. Fluid Mech. 285, 69–94.Google Scholar
Jiang, J.-Y. & Street, R. L. 1991 Modulated flows beneath wind-ruffled, mechanically generated water waves. J. Geophys. Res.-Oceans 96 (C2), 2711–2721.Google Scholar
Kawamura, T. 2000 Numerical investigation of turbulence near a sheared air–water interface. Part 2. Interaction of turbulent shear flow with surface waves. J. Mar. Sci. Technol. 5 (4), 161–175.Google Scholar
Kida, S. & Tanaka, M. 1994 Dynamics of vortical structures in a homogeneous shear flow. J. Fluid Mech. 274, 43–68.Google Scholar
Kim, J. & Moin, P. 1985 Application of a fractional-step method to incompressible Navier–Stokes equations. J. Comput. Phys. 59, 308–323.Google Scholar
Kirby, J. T. & Chen, T.-M. 1989 Surface waves on vertically sheared flows: approximate dispersion relations. J. Geophys. Res.-Oceans 94 (C1), 1013–1027.Google Scholar
Klewicki, J. C., Metzger, M. M., Kelner, E. & Thurlow, E. M. 1995 Viscous sublayer flow visualizations at R𝜃 ≃ 1 500 000. Phys. Fluids 7 (4), 857–863.Google Scholar
Komminaho, J., Lundbladh, A. & Johansson, A. V. 1996 Very large structures in plane turbulent Couette flow. J. Fluid Mech. 320, 259–285.Google Scholar
Kukulka, T., Plueddemann, A. J., Trowbridge, J. H. & Sullivan, P. P. 2009 Significance of Langmuir circulation in upper ocean mixing: comparison of observations and simulations. Geophys. Res. Lett. 36 (10), L10603.Google Scholar
Langmuir, I. 1938 Surface motion of water induced by wind. Science 87 (2250), 119–123.Google Scholar
Leibovich, S. 1977a Convective instability of stably stratified water in the ocean. J. Fluid Mech. 82 (03), 561–581.Google Scholar
Leibovich, S. 1977b 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 (04), 715–743.Google Scholar
Leibovich, S. 1980 On wave-current interaction theories of Langmuir circulations. J. Fluid Mech. 99 (04), 715–724.Google Scholar
Leibovich, S. 1983 The form and dynamics of Langmuir circulations. Annu. Rev. Fluid Mech. 15, 391–427.Google Scholar
Leibovich, S. & Paolucci, S. 1980 Energy stability of the Eulerian-mean motion in the upper ocean to three-dimensional perturbations. Phys. Fluids 23 (7), 1286–1290.Google Scholar
Leibovich, S. & Paolucci, S. 1981 The instability of the ocean to Langmuir circulations. J. Fluid Mech. 102, 141–167.Google Scholar
Lewis, D. M. 2005 A simple model of plankton population dynamics coupled with a LES of the surface mixed layer. J. Theor. Biol. 234 (4), 565–591.Google Scholar
Li, M. 2000 Estimating horizontal dispersion of floating particles in wind-driven upper ocean. Spill Sci. Technol. B. 6 (3–4), 255–261.Google Scholar
Li, M. & Garrett, C. 1993 Cell merging and the jet/downwelling ratio in Langmuir circulation. J. Mar. Res. 51 (4), 737–769.Google Scholar
Li, M., Garrett, C. & Skyllingstad, E. 2005 A regime diagram for classifying turbulent large eddies in the upper ocean. Deep-Sea Res. I 52 (2), 259–278.Google Scholar
Li, Q., Webb, A., Fox-Kemper, B., Craig, A., Danabasoglu, G., Large, W. G. & Vertenstein, M. 2016 Langmuir mixing effects on global climate: WAVEWATCH III in CESM. Ocean Model. 103, 145–160.Google Scholar
Longuet-Higgins, M. S. 1953 Mass transport in water waves. Phil. Trans. R. Soc. Lond. A 245 (903), 535–581.Google Scholar
Longuet-Higgins, M. S. 1986 Eulerian and Lagrangian aspects of surface waves. J. Fluid Mech. 173, 683–707.Google Scholar
Magnaudet, J. & Thais, L. 1995 Orbital rotational motion and turbulence below laboratory wind water waves. J. Geophys. Res.-Oceans 100 (C1), 757–771.Google Scholar
McWilliams, J. C., Huckle, E., Liang, J. & Sullivan, P. P. 2013 Langmuir turbulence in swell. J. Phys. Oceanogr. 44 (3), 870–890.Google Scholar
McWilliams, J. C. & Sullivan, P. P. 2000 Vertical mixing by Langmuir circulations. Spill Sci. Technol. B. 6 (3–4), 225–237.Google Scholar
McWilliams, J. C., Sullivan, P. P. & Moeng, C.-H. 1997 Langmuir turbulence in the ocean. J. Fluid Mech. 334, 1–30.Google Scholar
Melville, W. K., Shear, R. & Veron, F. 1998 Laboratory measurements of the generation and evolution of Langmuir circulations. J. Fluid Mech. 364, 31–58.Google Scholar
Meneveau, C., Lund, T. S. & Cabot, W. H. 1996 A Lagrangian dynamic subgrid-scale model of turbulence. J. Fluid Mech. 319, 353–385.Google Scholar
Moin, P. & Kim, J. 1985 The structure of the vorticity field in turbulent channel flow. Part 1. Analysis of instantaneous fields and statistical correlations. J. Fluid Mech. 155, 441–464.Google Scholar
Morris, S. C., Stolpa, S. R., Slaboch, P. E. & Klewicki, J. C. 2007 Near-surface particle image velocimetry measurements in a transitionally rough-wall atmospheric boundary layer. J. Fluid Mech. 580, 319–338.Google Scholar
Phillips, O. M. 1977 The Dynamics of the Upper Ocean, 2nd edn. Cambridge University Press.Google Scholar
Phillips, W. R. C. 2002 Langmuir circulations beneath growing or decaying surface waves. J. Fluid Mech. 469, 317–342.Google Scholar
Phillips, W. R. C. & Wu, Z. 1994 On the instability of wave-catalysed longitudinal vortices in strong shear. J. Fluid Mech. 272, 235–254.Google Scholar
Piomelli, U. & Balaras, E. 2002 Wall-layer models for large-eddy simulations. Annu. Rev. Fluid Mech. 34 (1), 349–374.Google Scholar
Polonichko, V. 1997 Generation of Langmuir circulation for nonaligned wind stress and the Stokes drift. J. Geophys. Res.-Oceans 102 (C7), 15773–15780.Google Scholar
Porté-Agel, F., Meneveau, C. & Parlange, M. B. 2000 A scale-dependent dynamic model for large-eddy simulation: application to a neutral atmospheric boundary layer. J. Fluid Mech. 415, 261–284.Google Scholar
Rabe, T. J., Kukulka, T., Ginis, I., Hara, T., Reichl, B. G., D’Asaro, E. A., Harcourt, R. R. & Sullivan, P. P. 2014 Langmuir turbulence under Hurricane Gustav (2008). J. Phys. Oceanogr. 45 (3), 657–677.Google Scholar
Rashidi, M., Hetsroni, G. & Banerjee, S. 1992 Wave–turbulence interaction in free-surface channel flows. Phys. Fluids A 4 (12), 2727–2738.Google Scholar
Shen, L., Zhang, X., Yue, D. K. P. & Triantafyllou, G. S. 1999 The surface layer for free-surface turbulent flows. J. Fluid Mech. 386, 167–212.Google Scholar
Skyllingstad, E. D. & Denbo, D. W. 1995 An ocean large-eddy simulation of Langmuir circulations and convection in the surface mixed layer. J. Geophys. Res.-Oceans 100 (C5), 8501–8522.Google Scholar
Stokes, G. 1847 On the theory of oscillatory waves. Trans. Camb. Phil. Soc. 8, 441–455.Google Scholar
Stoll, R. & Porté-Agel, F. 2006 Dynamic subgrid-scale models for momentum and scalar fluxes in large-eddy simulations of neutrally stratified atmospheric boundary layers over heterogeneous terrain. Water Resour. Res. 42 (1), W01409.Google Scholar
Sullivan, P. P. & McWilliams, J. C. 2010 Dynamics of winds and currents coupled to surface waves. Annu. Rev. Fluid Mech. 42, 19–42.Google Scholar
Sullivan, P. P., Romero, L., McWilliams, J. C. & Melville, W. K. 2012 Transient evolution of Langmuir turbulence in ocean boundary layers driven by hurricane winds and waves. J. Phys. Oceanogr. 42 (11), 1959–1980.Google Scholar
Swan, C., Cummins, I. P. & James, R. L. 2001 An experimental study of two-dimensional surface water waves propagating on depth-varying currents. Part 1. Regular waves. J. Fluid Mech. 428, 273–304.Google Scholar
Teixeira, M. A. C. & Belcher, S. E. 2002 On the distortion of turbulence by a progressive surface wave. J. Fluid Mech. 458, 229–267.Google Scholar
Teixeira, M. A. C. & Belcher, S. E. 2010 On the structure of Langmuir turbulence. Ocean Model. 31 (3–4), 105–119.Google Scholar
Tejada-Martínez, A. E. & Grosch, C. E. 2007 Langmuir turbulence in shallow water. Part 2. Large-eddy simulation. J. Fluid Mech. 576, 63–108.Google Scholar
Tejada-Martínez, A. E., Grosch, C. E., Gargett, A. E., Polton, J. A., Smith, J. A. & MacKinnon, J. A. 2009 A hybrid spectral/finite-difference large-eddy simulator of turbulent processes in the upper ocean. Ocean Model. 30 (2–3), 115–142.Google Scholar
Thorpe, S. A. 2004 Langmuir circulation. Annu. Rev. Fluid Mech. 36, 55–79.Google Scholar
Thorpe, S. A., Osborn, T. R., Farmer, D. M. & Vagle, S. 2003 Bubble clouds and Langmuir circulation: observations and models. J. Phys. Oceanogr. 33 (9), 2013–2031.Google Scholar
Tsai, W.-T., Chen, S.-M. & Moeng, C.-H. 2005 A numerical study on the evolution and structure of a stress-driven free-surface turbulent shear flow. J. Fluid Mech. 545, 163–192.Google Scholar
Tsukahara, T., Kawamura, H. & Shingai, K. 2006 DNS of turbulent Couette flow with emphasis on the large-scale structure in the core region. J. Turbul. 7, N19.Google Scholar
Van Roekel, L. P., Fox-Kemper, B., Sullivan, P. P., Hamlington, P. E. & Haney, S. R. 2012 The form and orientation of Langmuir cells for misaligned winds and waves. J. Geophys. Res.-Oceans 117 (C5), C05001.Google Scholar
Veron, F. & Melville, W. K. 2001 Experiments on the stability and transition of wind-driven water surfaces. J. Fluid Mech. 446, 25–65.Google Scholar
Veron, F., Melville, W. K. & Lenain, L. 2009 Measurements of ocean surface turbulence and wave–turbulence interactions. J. Phys. Oceanogr. 39 (9), 2310–2323.Google Scholar
Vivanco, F. & Melo, F. 2004 Experimental study of surface waves scattering by a single vortex and a vortex dipole. Phys. Rev. E 69 (2), 026307.Google Scholar
Wang, P. & Özgökmen, T. M. 2018 Langmuir circulation with explicit surface waves from moving-mesh modeling. Geophys. Res. Lett. 45 (1), 216–226.Google Scholar
Wu, Y. & Christensen, K. T. 2006 Population trends of spanwise vortices in wall turbulence. J. Fluid Mech. 568, 55–76.Google Scholar
Xuan, A. & Shen, L. 2019 A conservative scheme for simulation of free-surface turbulent and wave flows. Comput. Phys. 378, 18–43.Google Scholar
Yang, D., Chamecki, M. & Meneveau, C. 2014a Inhibition of oil plume dilution in Langmuir ocean circulation. Geophys. Res. Lett. 41 (5), 1632–1638.Google Scholar
Yang, D., Chen, B., Chamecki, M. & Meneveau, C. 2015 Oil plumes and dispersion in Langmuir, upper-ocean turbulence: large-eddy simulations and K-profile parameterization. J. Geophys. Res.-Oceans 120 (7), 4729–4759.Google 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, 62–99.Google Scholar
Yang, D., Meneveau, C. & Shen, L. 2014b Effect of downwind swells on offshore wind energy harvesting – A large-eddy simulation study. Renew. Energ. 70, 11–23.Google Scholar
Yang, D., Meneveau, C. & Shen, L. 2014c Large-eddy simulation of offshore wind farm. Phys. Fluids 26 (2), 025101.Google Scholar
Yang, D. & Shen, L. 2010 Direct-simulation-based study of turbulent flow over various waving boundaries. J. Fluid Mech. 650, 131–180.Google Scholar
Yang, D. & Shen, L. 2011 Simulation of viscous flows with undulatory boundaries. Part I. Basic solver. Comput. Phys. 230 (14), 5488–5509.Google Scholar
Zhang, Z., Chini, G. P., Julien, K. & Knobloch, E. 2015 Dynamic patterns in the reduced Craik–Leibovich equations. Phys. Fluids 27 (4), 046605.Google Scholar
Zhou, H.1999 Numerical simulation of Langmuir circulations in a wavy domain and its comparison with the Craik–Leibovich theory. PhD thesis, Stanford University.Google 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, 353–396.Google Scholar
Zikanov, O., Slinn, D. N. & Dhanak, M. R. 2003 Large-eddy simulations of the wind-induced turbulent Ekman layer. J. Fluid Mech. 495, 343–368.Google Scholar