Editorial Type:
Article
Article Type:
Research Article

Langmuir–Submesoscale Interactions: Descriptive Analysis of Multiscale Frontal Spindown Simulations

Peter E. Hamlington Department of Mechanical Engineering, University of Colorado Boulder, Boulder, Colorado

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Luke P. Van Roekel Northland College, Ashland, Wisconsin

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Baylor Fox-Kemper Cooperative Institute for Research in Environmental Sciences, University of Colorado Boulder, Boulder, Colorado, and Department of Geological Sciences, Brown University, Providence, Rhode Island

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Keith Julien Department of Applied Mathematics, University of Colorado Boulder, Boulder, Colorado

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Gregory P. Chini Department of Mechanical Engineering, University of New Hampshire, Durham, New Hampshire

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Print Publication:
01 Sep 2014
Collections:
Ocean Turbulence
DOI:
https://doi.org/10.1175/JPO-D-13-0139.1
Page(s):
2249–2272
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Abstract

The interactions between boundary layer turbulence, including Langmuir turbulence, and submesoscale processes in the oceanic mixed layer are described using large-eddy simulations of the spindown of a temperature front in the presence of submesoscale eddies, winds, and waves. The simulations solve the surface-wave-averaged Boussinesq equations with Stokes drift wave forcing at a resolution that is sufficiently fine to capture small-scale Langmuir turbulence. A simulation without Stokes drift forcing is also performed for comparison. Spatial and spectral properties of temperature, velocity, and vorticity fields are described, and these fields are scale decomposed in order to examine multiscale fluxes of momentum and buoyancy. Buoyancy flux results indicate that Langmuir turbulence counters the restratifying effects of submesoscale eddies, leading to small-scale vertical transport and mixing that is 4 times greater than in the simulations without Stokes drift forcing. The observed fluxes are also shown to be in good agreement with results from an asymptotic analysis of the surface-wave-averaged, or Craik–Leibovich, equations. Regions of potential instability in the flow are identified using Richardson and Rossby numbers, and it is found that mixed gravitational/symmetric instabilities are nearly twice as prevalent when Langmuir turbulence is present, in contrast to simulations without Stokes drift forcing, which are dominated by symmetric instabilities. Mixed layer depth calculations based on potential vorticity and temperature show that the mixed layer is up to 2 times deeper in the presence of Langmuir turbulence. Differences between measures of the mixed layer depth based on potential vorticity and temperature are smaller in the simulations with Stokes drift forcing, indicating a reduced incidence of symmetric instabilities in the presence of Langmuir turbulence.

Corresponding author address: Peter E. Hamlington, Department of Mechanical Engineering, University of Colorado Boulder, 427 UCB, Boulder, CO 80309. E-mail: peh@colorado.edu

This article is included in the Ocean Turbulence Special Collection.

Abstract

The interactions between boundary layer turbulence, including Langmuir turbulence, and submesoscale processes in the oceanic mixed layer are described using large-eddy simulations of the spindown of a temperature front in the presence of submesoscale eddies, winds, and waves. The simulations solve the surface-wave-averaged Boussinesq equations with Stokes drift wave forcing at a resolution that is sufficiently fine to capture small-scale Langmuir turbulence. A simulation without Stokes drift forcing is also performed for comparison. Spatial and spectral properties of temperature, velocity, and vorticity fields are described, and these fields are scale decomposed in order to examine multiscale fluxes of momentum and buoyancy. Buoyancy flux results indicate that Langmuir turbulence counters the restratifying effects of submesoscale eddies, leading to small-scale vertical transport and mixing that is 4 times greater than in the simulations without Stokes drift forcing. The observed fluxes are also shown to be in good agreement with results from an asymptotic analysis of the surface-wave-averaged, or Craik–Leibovich, equations. Regions of potential instability in the flow are identified using Richardson and Rossby numbers, and it is found that mixed gravitational/symmetric instabilities are nearly twice as prevalent when Langmuir turbulence is present, in contrast to simulations without Stokes drift forcing, which are dominated by symmetric instabilities. Mixed layer depth calculations based on potential vorticity and temperature show that the mixed layer is up to 2 times deeper in the presence of Langmuir turbulence. Differences between measures of the mixed layer depth based on potential vorticity and temperature are smaller in the simulations with Stokes drift forcing, indicating a reduced incidence of symmetric instabilities in the presence of Langmuir turbulence.

Corresponding author address: Peter E. Hamlington, Department of Mechanical Engineering, University of Colorado Boulder, 427 UCB, Boulder, CO 80309. E-mail: peh@colorado.edu

This article is included in the Ocean Turbulence Special Collection.

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  • Adcroft, A., and Coauthors, 2014: The MITgcm user manual. Department of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, MA, 470 pp. [Available online at http://mitgcm.org/public/r2_manual/latest/online_documents/manual.pdf.]

  • Alves, J., M. Banner, and I. Young, 2003: Revisiting the Pierson–Moskowitz asymptotic limits for fully developed wind waves. J. Phys. Oceanogr., 33, 1301–1323, doi:10.1175/1520-0485(2003)033<1301:RTPALF>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Belcher, S. E., and Coauthors, 2012: A global perspective on Langmuir turbulence in the ocean surface boundary layer. Geophys. Res. Lett.,39, L18605, doi:10.1029/2012GL052932.

  • Boccaletti, G., R. Ferrari, and B. Fox-Kemper, 2007: Mixed layer instabilities and restratification. J. Phys. Oceanogr., 37, 2228–2250, doi:10.1175/JPO3101.1.

    • Search Google Scholar
    • Export Citation

  • Capet, X., J. C. McWilliams, M. J. Molemaker, and A. F. Shchepetkin, 2008a: Mesoscale to submesoscale transition in the California Current system. Part I: Flow structure, eddy flux, and observational tests. J. Phys. Oceanogr., 38, 29–43, doi:10.1175/2007JPO3671.1.

    • Search Google Scholar
    • Export Citation

  • Capet, X., J. C. Mcwilliams, M. J. Molemaker, and A. F. Shchepetkin, 2008b: Mesoscale to submesoscale transition in the California current system. Part II: Frontal processes. J. Phys. Oceanogr., 38, 44–64, doi:10.1175/2007JPO3672.1.

    • Search Google Scholar
    • Export Citation

  • Craik, A. D. D., 1977: Generation of Langmuir circulations by an instability mechanism. J. Fluid Mech., 81, 209–223, doi:10.1017/S0022112077001980.

    • Search Google Scholar
    • Export Citation

  • Craik, A. D. D., and S. Leibovich, 1976: A rational model for Langmuir circulations. J. Fluid Mech., 73, 401–426, doi:10.1017/S0022112076001420.

    • Search Google Scholar
    • Export Citation

  • D’Asaro, E., and G. Dairiki, 1997: Turbulence intensity measurements in a wind-driven mixed layer. J. Phys. Oceanogr., 27, 2009–2022, doi:10.1175/1520-0485(1997)027<2009:TIMIAW>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • D’Asaro, E., C. Lee, L. Rainville, R. Harcourt, and L. Thomas, 2011: Enhanced turbulence and energy dissipation at ocean fronts. Science, 332, 318–322, doi:10.1126/science.1201515.

    • Search Google Scholar
    • Export Citation

  • Deardorff, J. W., 1980: Stratocumulus-capped mixed layers derives from a 3-dimensional model. Bound.-Layer Meteor., 18, 495–527, doi:10.1007/BF00119502.

    • Search Google Scholar
    • Export Citation

  • Donelan, M., J. Hamilton, and W. Hui, 1985: Directional spectra of wind-generated waves. Philos. Trans. Roy. Soc. London, A315, 509–562, doi:10.1098/rsta.1985.0054.

    • Search Google Scholar
    • Export Citation

  • Ferrari, R., and D. L. Rudnick, 2000: Thermohaline variability in the upper ocean. J. Geophys. Res., 105, 16 857–16 883, doi:10.1029/2000JC900057.

    • Search Google Scholar
    • Export Citation

  • Fox-Kemper, B., R. Ferrari, and R. W. Hallberg, 2008: Parameterization of mixed layer eddies. Part I: Theory and diagnosis. J. Phys. Oceanogr., 38, 1145–1165, doi:10.1175/2007JPO3792.1.

    • Search Google Scholar
    • Export Citation

  • Fox-Kemper, B., and Coauthors, 2011: Parameterization of mixed layer eddies. III: Implementation and impact in global ocean climate simulations. Ocean Modell., 39, 61–78, doi:10.1016/j.ocemod.2010.09.002.

    • Search Google Scholar
    • Export Citation

  • Gjaja, I., and D. D. Holm, 1996: Self-consistent Hamiltonian dynamics of wave mean-flow interaction for a rotating stratified incompressible fluid. Physica D, 98, 343–378, doi:10.1016/0167-2789(96)00104-2.

    • Search Google Scholar
    • Export Citation

  • Grant, A. L. M., and S. E. Belcher, 2009: Characteristics of Langmuir turbulence in the ocean mixed layer. J. Phys. Oceanogr., 39, 1871–1887, doi:10.1175/2009JPO4119.1.

    • Search Google Scholar
    • Export Citation

  • Haine, T. W. N., and J. C. Marshall, 1998: Gravitational, symmetric, and baroclinic instability of the ocean mixed layer. J. Phys. Oceanogr., 28, 634–658, doi:10.1175/1520-0485(1998)028<0634:GSABIO>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Haney, S., and Coauthors, 2012: Hurricane wake restratification rates of 1, 2 and 3-dimensional processes. J. Mar. Res., 70, 824–850, doi:10.1357/002224012806770937.

    • Search Google Scholar
    • Export Citation

  • Hanley, K. E., S. E. Belcher, and P. P. Sullivan, 2010: A global climatology of wind-wave interaction. J. Phys. Oceanogr., 40, 1263–1282, doi:10.1175/2010JPO4377.1.

    • Search Google Scholar
    • Export Citation

  • Harcourt, R. R., and E. A. D’Asaro, 2008: Large-eddy simulation of Langmuir turbulence in pure wind seas. J. Phys. Oceanogr., 38, 1542–1562, doi:10.1175/2007JPO3842.1.

    • Search Google Scholar
    • Export Citation

  • Holm, D., 1996: The ideal Craik-Leibovich equations. Physica D, 98, 415–441, doi:10.1016/0167-2789(96)00105-4.

  • Klein, P., and G. Lapeyre, 2009: The oceanic vertical pump induced by mesoscale and submesoscale turbulence. Annu. Rev. Mar. Sci., 1, 351–375, doi:10.1146/annurev.marine.010908.163704.

    • Search Google Scholar
    • Export Citation

  • Langmuir, I., 1938: Surface motion of water induced by wind. Science, 87, 119–123, doi:10.1126/science.87.2250.119.

  • Large, W., G. Danabasoglu, S. Doney, and J. McWilliams, 1997: Sensitivity to surface forcing and boundary layer mixing in a global ocean model: Annual-mean climatology. J. Phys. Oceanogr., 27, 2418–2447, doi:10.1175/1520-0485(1997)027<2418:STSFAB>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Li, K., G. P. Chini, Z. Zhang, and G. Flierl, 2012: Langmuir circulation: An agent for vertical restratification? J. Phys. Oceanogr., 42, 1945–1958, doi:10.1175/JPO-D-11-0225.1.

    • Search Google Scholar
    • Export Citation

  • Li, M., C. Garrett, and E. Skyllingstad, 2005: A regime diagram for classifying turbulent large eddies in the upper ocean. Deep-Sea Res. I, 52, 259–278, doi:10.1016/j.dsr.2004.09.004.

    • Search Google Scholar
    • Export Citation

  • Liang, J. H., J. C. McWilliams, P. P. Sullivan, and B. Baschek, 2011: Modeling bubbles and dissolved gases in the ocean. J. Geophys. Res.,116, C03015, doi:10.1029/2010JC006579.

  • Mahadevan, A., and A. Tandon, 2006: An analysis of mechanisms for submesoscale vertical motion at ocean fronts. Ocean Modell., 14, 241–256, doi:10.1016/j.ocemod.2006.05.006.

    • Search Google Scholar
    • Export Citation

  • Mahadevan, A., A. Tandon, and R. Ferrari, 2010: Rapid changes in mixed layer stratification driven by submesoscale instabilities and winds. J. Geophys. Res.,115, C03017, doi:10.1029/2008JC005203.

  • Malecha, Z., G. P. Chini, and K. Julien, 2013: A multiscale algorithm for simulating spatially-extended Langmuir circulation dynamics. J. Comput. Phys., 271, 131–150, doi:10.1016/j.jcp.2013.07.003.

    • Search Google Scholar
    • Export Citation

  • McWilliams, J. C., and P. Sullivan, 2000: Vertical mixing by Langmuir circulations. Spill Sci. Technol. Bull., 6, 225–237, doi:10.1016/S1353-2561(01)00041-X.

    • Search Google Scholar
    • Export Citation

  • McWilliams, J. C., and B. Fox-Kemper, 2013: Oceanic wave-balanced surface fronts and filaments. J. Fluid Mech., 730, 464–490, doi:10.1017/jfm.2013.348.

    • Search Google Scholar
    • Export Citation

  • McWilliams, J. C., P. Sullivan, and C. Moeng, 1997: Langmuir turbulence in the ocean. J. Fluid Mech., 334, 1–30, doi:10.1017/S0022112096004375.

    • Search Google Scholar
    • Export Citation

  • McWilliams, J. C., J. M. Restrepo, and E. M. Lane, 2004: An asymptotic theory for the interaction of waves and currents in coastal waters. J. Fluid Mech., 511, 135–178, doi:10.1017/S0022112004009358.

    • Search Google Scholar
    • Export Citation

  • Moeng, C.-H., 1984: A large-eddy-simulation model for the study of planetary boundary-layer turbulence. J. Atmos. Sci., 41, 2052–2062, doi:10.1175/1520-0469(1984)041<2052:ALESMF>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Noh, Y., H. Min, and S. Raasch, 2004: Large eddy simulation of the ocean mixed layer: The effects of wave breaking and Langmuir circulation. J. Phys. Oceanogr., 34, 720–735, doi:10.1175/1520-0485(2004)034<0720:LESOTO>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Özgökmen, T. M., A. C. Poje, P. F. Fischer, and A. C. Haza, 2011: Large eddy simulations of mixed layer instabilities and sampling strategies. Ocean Modell., 39, 311–331, doi:10.1016/j.ocemod.2011.05.006.

    • Search Google Scholar
    • Export Citation

  • Polton, J. A., and S. E. Belcher, 2007: Langmuir turbulence and deeply penetrating jets in an unstratified mixed layer. J. Geophys. Res., 112, C09020, doi:10.1029/2007JC004205.

    • Search Google Scholar
    • Export Citation

  • Shcherbina, A. Y., E. A. D’Asaro, C. M. Lee, J. M. Klymak, M. J. Molemaker, and J. C. McWilliams, 2013: Statistics of vertical vorticity, divergence, and strain in a developed submesoscale turbulence field. Geophys. Res. Lett., 40, 4706–4711, doi:10.1002/grl.50919.

    • Search Google Scholar
    • Export Citation

  • Skyllingstad, E. D., and D. Denbo, 1995: An ocean large-eddy simulation of Langmuir circulations and convection in the surface mixed-layer. J. Geophys. Res., 100, 8501–8522, doi:10.1029/94JC03202.

    • Search Google Scholar
    • Export Citation

  • Skyllingstad, E. D., and R. M. Samelson, 2012: Baroclinic frontal instabilities and turbulent mixing in the surface boundary layer. Part I: Unforced simulations. J. Phys. Oceanogr., 42, 1701–1716, doi:10.1175/JPO-D-10-05016.1.

    • Search Google Scholar
    • Export Citation

  • Smith, J., 1992: Observed growth of Langmuir circulation. J. Geophys. Res., 97, 5651–5664, doi:10.1029/91JC03118.

  • Spall, M., 1997: Baroclinic jets in confluent flow. J. Phys. Oceanogr., 27, 1054–1071, doi:10.1175/1520-0485(1997)027<1054:BJICF>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Stone, P. H., 1966: On non-geostrophic baroclinic stability. J. Atmos. Sci., 23, 390–400, doi:10.1175/1520-0469(1966)023<0390:ONGBS>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Sullivan, P. P., and J. C. McWilliams, 2010: Dynamics of winds and currents coupled to surface waves. Annu. Rev. Fluid Mech., 42, 19–42, doi:10.1146/annurev-fluid-121108-145541.

    • Search Google Scholar
    • Export Citation

  • Sullivan, P. P., J. C. McWilliams, and C. H. Moeng, 1994: A subgrid-scale model for large-eddy simulation of planetary boundary-layer flows. Bound.-Layer Meteor., 71, 247–276, doi:10.1007/BF00713741.

    • Search Google Scholar
    • Export Citation

  • Sullivan, P. P., J. C. McWilliams, and W. K. Melville, 2004: The oceanic boundary layer driven by wave breaking with stochastic variability. Part 1. Direct numerical simulations. J. Fluid Mech., 507, 143–174, doi:10.1017/S0022112004008882.

    • Search Google Scholar
    • Export Citation

  • Sullivan, P. P., J. C. McWilliams, and W. K. Melville, 2007: Surface gravity wave effects in the oceanic boundary layer: Large-eddy simulation with vortex force and stochastic breakers. J. Fluid Mech., 593, 405–452, doi:10.1017/S002211200700897X.

    • Search Google Scholar
    • Export Citation

  • Taylor, J. R., and R. Ferrari, 2010: Buoyancy and wind-driven convection at mixed layer density fronts. J. Phys. Oceanogr., 40, 1222–1242, doi:10.1175/2010JPO4365.1.

    • Search Google Scholar
    • Export Citation

  • Thomas, L. N., 2005: Destruction of potential vorticity by winds. J. Phys. Oceanogr., 35, 2457–2466, doi:10.1175/JPO2830.1.

  • Thomas, L. N., and C. M. Lee, 2005: Intensification of ocean fronts by down-front winds. J. Phys. Oceanogr., 35, 1086–1102, doi:10.1175/JPO2737.1.

    • Search Google Scholar
    • Export Citation

  • Thomas, L. N., and J. R. Taylor, 2010: Reduction of the usable wind-work on the general circulation by forced symmetric instability. Geophys. Res. Lett.,37, L18606, doi:10.1029/2010GL044680.

  • Thomas, L. N., J. R. Taylor, R. Ferrari, and T. M. Joyce, 2013: Symmetric instability in the Gulf Stream. Deep-Sea Res. II, 91, 96–110, doi:10.1016/j.dsr2.2013.02.025.

    • Search Google Scholar
    • Export Citation

  • Thorpe, S. A., 2004: Langmuir circulation. Annu. Rev. Fluid Mech., 36, 55–79, doi:10.1146/annurev.fluid.36.052203.071431.

  • Van Roekel, L. P., B. Fox-Kemper, P. P. Sullivan, P. E. Hamlington, and S. R. Haney, 2012a: The form and orientation of Langmuir cells for misaligned winds and waves. J. Geophys. Res.,117, C05001, doi:10.1029/2011JC007516.

  • Van Roekel, L. P., P. E. Hamlington, and B. Fox-Kemper, 2012b: Multiscale simulations of Langmuir cells and submesoscale eddies using XSEDE resources. Proc. First Conf. of the Extreme Science and Engineering Discovery Environment: Bridging from the eXtreme to the campus and beyond, Chicago, IL, National Science Foundation, Article 20, doi:10.1145/2335755.2335816.

  • Webb, A., and B. Fox-Kemper, 2011: Wave spectral moments and Stokes drift estimation. Ocean Modell., 40, 273–288, doi:10.1016/j.ocemod.2011.08.007.

    • Search Google Scholar
    • Export Citation

  • Weller, R., and J. Price, 1988: Langmuir circulation within the oceanic mixed layer. Deep-Sea Res., 35A, 711–747, doi:10.1016/0198-0149(88)90027-1.

    • Search Google Scholar
    • Export Citation
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