Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-11-22T23:22:29.887Z Has data issue: false hasContentIssue false
  • English
  • Français

Localizing effect of Langmuir circulations on small-scale turbulence in shallow water

Published online by Cambridge University Press:  17 April 2020

Bing-Qing Deng Open the ORCID record for Bing-Qing Deng [Opens in a new window] ,
Zixuan Yang Open the ORCID record for Zixuan Yang [Opens in a new window] ,
Anqing Xuan Open the ORCID record for Anqing Xuan [Opens in a new window]  and
Lian Shen Open the ORCID record for Lian Shen [Opens in a new window]
Bing-Qing Deng
Affiliation:
Department of Mechanical Engineering and St. Anthony Falls Laboratory, University of Minnesota, Minneapolis, MN55414, USA
Zixuan Yang
Affiliation:
Department of Mechanical Engineering and St. Anthony Falls Laboratory, University of Minnesota, Minneapolis, MN55414, USA Institute of Mechanics, Chinese Academy of Sciences, 100190Beijing, PR China
Anqing Xuan
Affiliation:
Department of Mechanical Engineering and St. Anthony Falls Laboratory, University of Minnesota, Minneapolis, MN55414, USA
Lian Shen*
Affiliation:
Department of Mechanical Engineering and St. Anthony Falls Laboratory, University of Minnesota, Minneapolis, MN55414, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Wall-resolved and wall-modelled large-eddy simulations are performed to study the localizing effect of Langmuir cells (LCs) on small-scale background turbulence in shallow water. The total velocity fluctuations are decomposed into an LC content extracted by streamwise averaging and a background turbulence part. Based on the large-scale motions of LCs, the spanwise domain is divided into three regions dominated by the upwelling, spanwise and downwelling flows of LCs, respectively. The localized Reynolds stresses $\langle u_{i}^{T}u_{j}^{T}\rangle _{xt}$ in different spanwise regions are compared to show the localizing effects of the LCs on the background turbulence quantitatively, where $u_{1}^{T}$ (or $u^{T}$), $u_{2}^{T}$ (or $v^{T}$) and $u_{3}^{T}$ (or $w^{T}$) represent the streamwise, vertical and spanwise components of the background turbulence velocity, respectively, and $\langle \cdot \rangle _{xt}$ denotes time and streamwise averaging. It is shown that the magnitudes of the localized Reynolds stresses in different spanwise regions vary significantly. The transport equations of the localized Reynolds stresses are then analysed to investigate the mechanisms underlying the localizing effects. It is discovered that the difference in the energy production correlated to the shear of the LC content among different regions is the key factor that leads to the localization of background turbulence. In addition, the energy production correlated to the shear of the mean flow, the energy redistribution due to the pressure–strain correlation, and the interaction between the localized Reynolds stresses and the shear of the Stokes drift also play important roles. Based on the results obtained from the analysis of the transport equations, predictive models are proposed for the localizing effects, which assess the spatial dependence of the Boussinesq model for background turbulence in coastal Langmuir turbulence. These models show good scaling performance of $\langle u^{T}u^{T}\rangle _{xt}$ near the water bottom and of $\langle -u^{T}v^{T}\rangle _{xt}$, $\langle -u^{T}w^{T}\rangle _{xt}$ and $\langle -v^{T}w^{T}\rangle _{xt}$ in the central region of the water column under various flow conditions with different values of the Reynolds number, turbulent Langmuir number and wavenumber.

JFM classification

Turbulent Flows: Turbulence simulation Turbulent Flows: Turbulent boundary layers
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 893 , 25 June 2020 , A6
Copyright
© The Author(s), 2020. 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.)

References

Akan, C., Tejada-Martínez, A. E., Grosch, C. E. & Martinat, G. 2013 Scalar transport in large-eddy simulation of Langmuir turbulence in shallow water. Cont. Shelf Res. 55, 1–16.CrossRefGoogle Scholar
Anderson, W. 2016 Amplitude modulation of streamwise velocity fluctuations in the roughness sublayer: evidence from large-eddy simulations. J. Fluid Mech. 789, 567–588.CrossRefGoogle Scholar
Assaf, G., Gerard, R. & Gordon, A. L. 1971 Some mechanisms of oceanic mixing revealed in aerial photographs. J. Geophys. Res. 76, 6550–6572.CrossRefGoogle Scholar
Balaras, E., Benocci, C. & Piomelli, U. 1995 Finite-difference computations of high Reynolds number flows using the dynamic subgrid-scale model. Theor. Comput. Fluid Dyn. 7, 207–216.CrossRefGoogle Scholar
Barstow, S. F. 1983 The ecology of Langmuir circulation: a review. Mar. Environ. Res. 9 (4), 211–236.CrossRefGoogle Scholar
Belcher, S. E., Grant, A. L., Hanley, K. E., Fox-Kemper, B., Van-Roekel, L., Sullivan, P. P., Large, W. G., Brown, A., Hines, A., Calvert, D. et al. 2011 A global perspective on Langmuir turbulence in the ocean surface boundary layer. Geophys. Res. Lett. 39 (18), L18605.Google Scholar
Bernardini, M., Pirozzoli, S. & Orlandi, P. 2014 Velocity statistics in turbulent channel flow up to Re 𝜏 = 4000. J. Fluid Mech. 742, 171–191.CrossRefGoogle Scholar
Chapman, D. R. 1979 Computational aerodynamics development and outlook. AIAA J. 17, 1293–1313.CrossRefGoogle Scholar
Choi, H. & Moin, P. 2012 Grid-point requirements for large eddy simulation: Chapman’s estimates revisited. Phys. Fluids 24, 011702.CrossRefGoogle Scholar
Craik, A. D. D. & Leibovich, S. 1976 A rational model for Langmuir circulations. J. Fluid Mech. 73, 401–426.CrossRefGoogle Scholar
Dai, Y. J., Huang, W. X. & Xu, C. X. 2016 Effects of Taylor–Görtler vortices on turbulent flows in a spanwise-rotating channel. Phys. Fluids 28 (11), 115104.CrossRefGoogle Scholar
D’Asaro, E. A. 2014 Turbulence in the upper-ocean mixed layer. Annu. Rev. Mar. Sci. 6, 101–115.CrossRefGoogle ScholarPubMed
Deng, B. Q., Huang, W. X. & Xu, C. X. 2016 Origin of effectiveness degradation in active drag reduction control of turbulent channel flow at Re 𝜏 = 1000. J. Turbul. 17, 758–786.CrossRefGoogle 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.CrossRefGoogle Scholar
Dethleff, D. & Kempema, E. W. 2007 Langmuir circulation driving sediment entrainment into newly formed ice: tank experiment results with application to nature (Lake Hattie, United States; Kara Sea, Siberia). J. Geophys. Res. 112, C02004.CrossRefGoogle Scholar
Dierssen, H. M., Zimmerman, R. C., Drake, L. A. & Burdige, D. J. 2009 Potential export of unattached benthic macroalgae to the deep sea through wind-driven Langmuir circulation. Geophys. Res. Lett. 36, L04602.CrossRefGoogle Scholar
Farmer, D. & Li, M. 1995 Patterns of bubble clouds organized by Langmuir circulation. J. Phys. Oceanogr. 25, 1426–1440.2.0.CO;2>CrossRefGoogle Scholar
Gargett, A., Wells, J., Tejada-Martínez, A. E. & Grosch, C. E. 2004 Langmuir supercells: a mechanism for sediment resuspension and transport in shallow seas. Science 306, 1925–1928.CrossRefGoogle ScholarPubMed
Gargett, A. E. & Grosch, C. E. 2014 Turbulence process domination under the combined forcings of wind stress, the Langmuir vortex force, and surface cooling. J. Phys. Oceanogr. 44 (1), 44–67.CrossRefGoogle Scholar
Gargett, A. E., Savidge, D. K. & Wells, J. R. 2014 Anatomy of a Langmuir supercell event. J. Mar. Res. 72 (3), 127–163.CrossRefGoogle Scholar
Gargett, A. E. & Wells, J. R. 2007 Langmuir turbulence in shallow water. Part 1. Observations. J. Fluid Mech. 576, 27–61.CrossRefGoogle Scholar
Gemmrich, J. R. & Farmer, D. M. 1999 Near-surface turbulence and thermal structure in a wind-driven sea. J. Phys. Oceanogr. 29 (3), 480–499.2.0.CO;2>CrossRefGoogle Scholar
Gerbi, G. P., Trowbridge, J. H., Terray, E. A., Plueddemann, A. J. & Kukulka, T. 2009 Observations of turbulence in the ocean surface boundary layer: energetics and transport. J. Phys. Oceanogr. 39 (5), 1077–1096.CrossRefGoogle Scholar
Germano, M., Piomelli, U., Moin, P. & Cabot, W. H. 1991 A dynamic subgrid-scale eddy viscosity model. Phys. Fluids A 3, 1760–1765.CrossRefGoogle Scholar
Gloshan, R., Tejada-Martínez, A. E., Juha, M. J. & Bazilevs, Y. 2017 LES and RANS simulation of wind- and wave-forced oceanic turbulent boundary layers in shallow water with wall modeling. Comput. Fluids 142, 96–108.CrossRefGoogle Scholar
Grosch, C. E. & Gargett, A. E. 2016 Why do LES of Langmuir supercells not include rotation? J. Phys. Oceanogr. 46 (12), 3595–3597.CrossRefGoogle Scholar
Harcourt, R. R. 2013 A second-moment closure model of Langmuir turbulence. J. Phys. Oceanogr. 43, 675–697.CrossRefGoogle Scholar
Howland, M. F. & Yang, X. I. A. 2018 Dependence of small-scale energetics on large scales in turbulent flows. J. Fluid Mech. 852, 641–662.CrossRefGoogle Scholar
Hoyas, S. & Jiménez, J. 2008 Reynolds number effects on the Reynolds-stress budgets in turbulent channels. Phys. Fluids 20, 101511.CrossRefGoogle Scholar
Hutchins, N. & Marusic, I. 2007 Large-scale influences in near-wall turbulence. Proc. R. Soc. Lond. A 365, 647–664.Google ScholarPubMed
Inoue, M., Mathis, R., Marusic, I. & Pullin, D. I. 2012 Inner-layer intensities for the flat-plate turbulent boundary layer combining a predictive wall-model with large-eddy simulations. Phys. Fluids 24, 075102.CrossRefGoogle Scholar
Jimenez, J. 2012 Cascades in wall-bounded turbulence. Annu. Rev. Fluid Mech. 44, 27–45.CrossRefGoogle Scholar
Kim, J. & Moin, P. 1985 Application of a fractional-step method to incompressible Navier–Stokes equations. J. Comput. Phys. 59, 308–323.CrossRefGoogle Scholar
Kukulka, T. & Harcourt, R. R. 2017 Influence of Stokes drift decay scale on Langmuir turbulence. J. Phys. Oceanogr. 47 (7), 1637–1656.CrossRefGoogle Scholar
Kukulka, T., Plueddemann, A. J. & Sullivan, P. P. 2012 Nonlocal transport due to Langmuir circulation in a coastal ocean. J. Geophys. Res. 117, C12007.CrossRefGoogle Scholar
Kukulka, T., Plueddemann, A. J., Trowbridge, J. H. & Sullivan, P. P. 2011 The influence of crosswind tidal currents on Langmuir circulation in a shallow ocean. J. Geophys. Res. 116, C08005.CrossRefGoogle Scholar
Langmuir, I. 1938 Surface motion of water induced by wind. Science 87, 119–123.CrossRefGoogle ScholarPubMed
Leibovich, S. 1977 On the evolution of the system of wind drift currents and Langmuir circulations in the ocean. J. Fluid Mech. 79, 715–743.CrossRefGoogle Scholar
Leibovich, S. 1983 The form and dynamics of Langmuir circulations. Annu. Rev. Fluid Mech. 15, 391–427.CrossRefGoogle Scholar
Li, S., Li, M., Gerbi, G. P. & Song, J. B. 2013 Roles of breaking waves and Langmuir circulation in the surface boundary layer of a coastal ocean. J. Geophys. Res. 118 (10), 5173–5187.CrossRefGoogle Scholar
Lilly, D. K. 1992 A proposed modification of the Germano subgrid-scale closure method. Phys. Fluids 4, 633–635.CrossRefGoogle Scholar
Martinat, G., Grosch, C. E. & Gatski, T. B. 2014 Modeling of Langmuir circulation: triple decomposition of the Craik–Leibovich model. Flow Turbul. Combust. 92 (1–2), 395–411.CrossRefGoogle Scholar
Martinat, G., Xu, Y., Grosch, C. E. & Tejada-Martínez, A. E. 2011 LES of turbulent surface shear stress and pressure-gradient-driven flow on shallow continental shelves. Ocean Dyn. 61 (9), 1369–1390.Google Scholar
Mathis, R., Hutchins, N. & Marusic, I. 2009 Large-scale amplitude modulation of the small-scale structures in turbulent boundary layers. J. Fluid Mech. 628, 311–337.CrossRefGoogle Scholar
McWilliams, J. C., Sullivan, P. P. & Moeng, C. H. 1997 Langmuir turbulence in the ocean. J. Fluid Mech. 334, 1–30.CrossRefGoogle Scholar
Papavassiliou, D. V. & Hanratty, T. J. 1997 Interpretation of large-scale structures observed in a turbulent plane Couette flow. Intl J. Heat Fluid Flow 18, 55–69.CrossRefGoogle Scholar
Piomelli, U. & Balaras, E. 2002 Wall-layer models for large-eddy simulations. Annu. Rev. Fluid Mech. 34, 349–374.CrossRefGoogle Scholar
Pope, S. B. 2001 Turbulent Flows. Cambridge University Press.Google Scholar
Reynolds, W. C. & Hussain, A. K. 1972 The mechanics of an organized wave in turbulent shear flow. Part 3. Theoretical models and comparisons with experiments. J. Fluid Mech. 54 (2), 263–288.CrossRefGoogle Scholar
Salesky, S. T. & Anderson, W. 2018 Buoyancy effects on large-scale motions in convective atmospheric boundary layers: implications for modulation of near-wall processes. J. Fluid Mech. 856, 133–168.CrossRefGoogle Scholar
Savidge, D. K. & Gargett, A. E. 2017 Langmuir supercells on the middle shelf of the South Atlantic Bight: 1. Cell structure. J. Mar. Res. 75 (2), 49–79.CrossRefGoogle Scholar
Scott, J. T., Myer, G. E., Stewart, R. & Walther, E. G. 1969 On the mechanism of Langmuir circulations and their role in epilimnion mixing. Limnol. Oceanogr. 14, 493–503.CrossRefGoogle Scholar
Shrestha, K. & Anderson, W. 2019 Coastal Langmuir circulations induced phase-locked modulation of bathymetric stress. Environ. Fluid Mech., 1–12.Google Scholar
Shrestha, K., Anderson, W. & Kuehl, J. 2018 Langmuir turbulence in coastal zones: structure and length scales. J. Phys. Oceanogr. 48, 1089–1115.CrossRefGoogle Scholar
Shrestha, K., Tejada-Martinez, A. & Kuehl, J. 2019 Orientation of coastal-zone Langmuir cells forced by wind, wave and mean current at variable obliquity. J. Fluid Mech. 879, 716–743.CrossRefGoogle Scholar
Sinha, N., Tejada-Martínez, A. E., Akan, C. & Grosch, C. E. 2015 Toward a K-profile parameterization of Langmuir turbulence in shallow coastal shelves. J. Phys. Oceanogr. 45 (12), 2869–2895.CrossRefGoogle 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. 100, 8501–8522.CrossRefGoogle Scholar
Smargorinsky, J. 1963 General circulation experiments with the primitive equations: I. The basic experiment. Mon. Weath. Rev. 91, 99–164.2.3.CO;2>CrossRefGoogle Scholar
Smith, A. J., McKeon, B. J. & Marusic, I. 2011 High-Reynolds number wall turbulence. Annu. Rev. Fluid Mech. 43, 353–375.CrossRefGoogle Scholar
Smith, J. A. 1992 Observed growth of Langmuir circulation. J. Geophys. Res. 97, 5651–5664.CrossRefGoogle Scholar
Smith, J. A. 2001 Fluid Mechanics and the Environment: Dynamical Approaches. Springer.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.CrossRefGoogle Scholar
Takagaki, N., Kurose, R., Tsujimoto, Y., Komori, S. & Takahashi, K. 2015 Effects of turbulent eddies and Langmuir circulations on scalar transfer in a sheared wind-driven liquid flow. Phys. Fluids 27, 016603.CrossRefGoogle Scholar
Tejada-Martínez, A. E., Akan, C., Sinha, N., Grosch, C. E. & Martinat, G. 2013 Surface dynamics in LES of full-depth Langmuir circulation in shallow water. Phys. Scr. 2013, 014008.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.CrossRefGoogle Scholar
Tejada-Martínez, A. E., Grosch, C. E., Sinha, N., Akan, C. & Martinat, G. 2012 Disruption of the bottom log layer in large-eddy simulations of full-depth Langmuir circulation. J. Fluid Mech. 699, 79–93.CrossRefGoogle Scholar
Thorpe, S. A. 1992 The breakup of Langmuir circulation and the instability of an array of vortices. J. Phys. Oceanogr. 22, 350–360.2.0.CO;2>CrossRefGoogle Scholar
Thorpe, S. A. 2004 Langmuir circulation. Annu. Rev. Fluid Mech. 36, 55–79.CrossRefGoogle Scholar
Walker, R., Tejada-Martínez, A. E. & Grosch, C. E. 2016 Large-eddy simulation of a coastal ocean under the combined effects of surface heat fluxes and full-depth Langmuir circulation. J. Phys. Oceanogr. 46 (8), 2411–2436.CrossRefGoogle Scholar
Weller, R. A. & Price, J. F. 1988 Langmuir circulation within the oceanic mixed layer. Deep Sea Res. A 35, 711–747.CrossRefGoogle Scholar
Yin, G., Huang, W. X. & Xu, C. X. 2018 Prediction of near-wall turbulence using minimal flow unit. J. Fluid Mech. 841, 654–673.CrossRefGoogle Scholar
Supplementary material: File

Deng et al. supplementary material

Deng et al. supplementary material

Download Deng et al. supplementary material(File)
File 1.9 MB