Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-26T13:09:17.079Z Has data issue: false hasContentIssue false
  • English
  • Français

Orientation of coastal-zone Langmuir cells forced by wind, wave and mean current at variable obliquity

Published online by Cambridge University Press:  01 October 2019

K. Shrestha ,
W. Anderson Open the ORCID record for W. Anderson [Opens in a new window] ,
A. Tejada-Martinez Open the ORCID record for A. Tejada-Martinez [Opens in a new window]  and
J. Kuehl
K. Shrestha
Affiliation:
Mechanical Engineering Department, University of Texas at Dallas, TX 75080, USA
W. Anderson*
Affiliation:
Mechanical Engineering Department, University of Texas at Dallas, TX 75080, USA
A. Tejada-Martinez
Affiliation:
Department of Civil and Environmental Engineering, University of South Florida, FL 33620, USA
J. Kuehl
Affiliation:
Mechanical Engineering Department, University of Delaware, DE 19716, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Langmuir circulation, a key turbulent process in the upper ocean, is mechanistically driven and sustained by imposed atmospheric wind stress and surface wave drift. In addition, and specifically in coastal zones, the presence of a mean current – whether associated with tidal currents or large-scale eddies – generates bottom-boundary-layer shear, which further modulates the physical attributes of coastal-zone Langmuir turbulence. We show that the presence of bottom-boundary-layer shear generated by oblique forcing between the mean current, atmospheric drag, and monochromatic wave field direction changes the orientation of the resultant, large-scale Langmuir cells. A model to predict this resultant orientation, based on salient parameters defining the forcing obliquity, is proposed. We also perform a systematic parametric study to isolate the ‘turning’ influence of salient parameters, which reveals that the resultant Langmuir cell orientation is always intermediate to the imposed forces. In order to provide a rigorous basis for the results, we study terms responsible for sustenance of streamwise vorticity, and provide a theoretical justification for the observed results.

JFM classification

Geophysical and Geological Flows: Ocean processes Turbulent Flows: Turbulence simulation
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 879 , 25 November 2019 , pp. 716 - 743
Check for updates
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

Albertson, J. & Parlange, M. 1999 Surface length scales and shear stress: implications for land-atmosphere interaction over complex terrain. Water Resour. Res. 35, 2121–2132.10.1029/1999WR900094Google Scholar
Anderson, W. & Meneveau, C. 2011 Dynamic large-eddy simulation model for boundary layer flow over multiscale, fractal-like surface. J. Fluid Mech. 679, 288–314.10.1017/jfm.2011.137Google Scholar
Bou-Zeid, E., Meneveau, C. & Parlange, M. B. 2005 A scale-dependent Lagrangian dynamic model for large eddy simulation of complex turbulent flows. Phys. Fluids 17, 025105.Google Scholar
Cox, S. 1997 Onset of Langmuir circulation when shear flow and Stokes drift are not parallel. Fluid Dyn. Res. 19, 149–167.10.1016/S0169-5983(97)00035-XGoogle Scholar
Craik, A. D. D. 1977 The generation of Langmuir circulations by an instability mechanism. J. Fluid Mech. 81, 209–223.Google Scholar
Craik, A. D. D. & Leibovich, S. 1976 A rational model for Langmuir circulation. J. Fluid Mech. 73, 401–426.10.1017/S0022112076001420Google Scholar
Deng, B., 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
DiMarco, S. F., Howard, M. K. & Reid, R. O. 2000 Seasonal variation of wind-driven diurnal cycling on the Texas–Louisiana continental shelf. Geophys. Res. Lett. 21, 1017–1020.10.1029/1999GL010491Google 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, 341–356.10.1175/BAMS-88-3-341Google Scholar
Fan, Y., Jarosz, E., Yu, Z., Rogers, W. E., Jensen, T. G. & Liang, J.-H. 2018 Langmuir turbulence in horizontal salinity gradient. Ocean Model. 129, 93–103.10.1016/j.ocemod.2018.07.010Google Scholar
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, 44–67.Google Scholar
Gargett, A. E. & Wells, J. R. 2007 Langmuir turbulence in shallow water. Part 1. Observations. J. Fluid Mech. 576, 27–61.10.1017/S0022112006004575Google Scholar
Gargett, A. E., Wells, J. R., Tejada-Martínez, A. E. & Grosch, C. E. 2004 Langmuir supercells: a mechanism for sediment resuspension and transport in shallow seas. Science 306, 1925–1928.Google Scholar
Gerbi, P. G., Trowbridge, J. H., Terry, E. A., Plueddemann, A. J. & Kukulka, T. 2009 Observations of turbulence in the ocean surface boundary layer: energetics and transport. J. Phys. Oceanogr. 39, 1077–1096.10.1175/2008JPO4044.1Google 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, 3148–3171.Google Scholar
Graham, J. & Meneveau, C. 2012 Modeling turbulent flow over fractal trees using renormalized numerical simulation: alternate formulations and numerical experiments. Phys. Fluids 24, 125105.10.1063/1.4772074Google Scholar
Hamlington, P. E., VanRoekel, L. P., Fox-Kemper, B., Julien, K. & Chini, G. P. 2014 Langmuir-submesoscale interactions: descriptive analysis of multiscale frontal spindown simulations. J. Phys. Oceanogr. 44, 2249–2272.Google Scholar
Harcourt, R. R. 2013 A second-moment closure model of Langmuir turbulence. J. Phys. Oceanogr. 43, 673–697.Google Scholar
Kim, J., Moin, P. & Moser, R. 1987 Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177, 133–166.Google Scholar
Kuehl, J., DiMarco, S., Spencer, L. & Guinasso, N. 2014 Application of the smooth orthogonal decomposition to oceanographic datasets. Geophys. Res. Lett. 41, 3966–3971.Google Scholar
Kuehl, J. & Sheremet, V. A. 2014 Two-layer gap-leaping oceanic boundary currents: experimental investigation. J. Fluid Mech. 740, 97–113.10.1017/jfm.2013.645Google Scholar
Kukulka, T., Pleuddemann, A. & Sullivan, P. 2012 Nonlocal transport due to Langmuir circulation in a coastal ocean. J. Geophys. Res. 117, C12007.10.1029/2012JC008340Google Scholar
Kukulka, T., Pleuddemann, A., Trowbridge, J. H. & Sullivan, P. 2011 The influence of crosswind tidal currents on Langmuir circulation in a shallow ocean. J. Geophys. Res. 116, C08005.10.1029/2011JC006971Google Scholar
Leibovich, S. 1977 Convective instability of stably stratified water in the ocean. J. Fluid Mech. 82, 561–585.10.1017/S0022112077000846Google Scholar
Leibovich, S. 1983 The form and dynamics of Langmuir circulations. Annu. Rev. Fluid Mech. 15, 391–427.Google Scholar
Leonardi, S., Orlandi, P., Djenidi, L. & Antonia, R. A. 2004 Structure of turbulent channel flow with square bars on one wall. Intl J. Heat Fluid Flow 25, 384–392.Google 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, 5173–5187.Google Scholar
Lipphardt, B. L., Poje, A. C. Jr, Kirwan, A. D., Kantha, L. & Zweng, M. 2008 Death of three Loop Current rings. J. Mar. Res. 66, 25–60.Google Scholar
Liu, S., Kermani, A., Shen, L. & Yue, D. K. P. 2009 Investigation of coupled air–water turbulent boundary layers using direct numerical simulations. Phys. Fluids 21, 062108.Google 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, 1369–1390.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
Meneveau, C. & Katz, J. 2000 Scale-invariance and turbulence models for large-eddy simulation. Annu. Rev. Fluid Mech. 32 (1), 1–32.Google Scholar
Orszag, S. 1970 Transform method for calculation of vector coupled sums: application to the spectral form of the vorticity equation. J. Atmos. Sci. 27, 890–895.Google Scholar
Oye, L. Y., Ezer, T. & Lee, H. C. 2005 Loop current, rings and related circulation in the Gulf of Mexico: a review of numerical models and future challenges. Geophys. Monogr. Ser. 161, 31–56.Google Scholar
Phillips, O. M. 1966 The Dynamics of the Upper Ocean. Cambridge University Press.Google Scholar
Polonichko, V. 1997 Generation of Langmuir circulation for nonaligned wind stress and the Stokes drift. J. Geophys. Res. 102, 773–780.10.1029/97JC00460Google Scholar
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.Google 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, 49–79.Google Scholar
Sherwood, C. R., Lacey, J. R. & Voulgaris, G. 2006 Shear velocity estimates on the inner shelf off Grays Harbor, Washington, USA. Cont. Shelf Res. 26, 1995–2018.Google Scholar
Shrestha, K., Anderson, W. & Kuehl, J. 2018 Langmuir turbulence in coastal zones: structure and length scales. J. Phys. Oceanogr. 48, 1089–1115.Google Scholar
Sinha, N., Tejada-Martínez, A. E. & Akan, C. 2015 Toward a K-profile parameterization of Langmuir turbulence in shallow coastal shelves. J. Phys. Oceanogr. 45, 2869–2895.Google Scholar
Spencer, L. J., DiMarco, S. F., Wang, Z., Kuehl, J. J. & Brooks, D. A. 2016 Asymmetric oceanic response to a hurricane: deepwater observations during Hurricane Isaac. J. Geophys. Res. 121, 7619–7649.Google Scholar
Sternberg, W. R. 1968 Friction factors in tidal channels with differing bed roughness. Mar. Geol. 6, 243–260.Google Scholar
Stevens, R. J. A. M., Wilczek, M. & Meneveau, C. 2014 Large-eddy simulation study of the logarithmic law for second- and higher-order moments in turbulent wall-bounded flow. J. Fluid Mech. 757, 888–907.10.1017/jfm.2014.510Google 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 (11), 4001–4027.10.1175/JAS-D-14-0095.1Google Scholar
Suzuki, N. & Fox-Kemper, B. 2016 Understanding stokes forces in the wave-averaged equations. J. Geophys. Res. 121, 3579–3596.Google Scholar
Tejada-Martínez, A. E., Akan, C., Grosch, N., Sinha, C. E. & Martinat, G. 2013 Surface dynamics in LES of full-depth Langmuir circulation in shallow water. Phys. Scr. 2013 (T155), 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.Google Scholar
Tejada-Martínez, A. E., Grosch, C. E., Sinha, N., Akan, C. & Martinat, G. 2012 Disruption of bottom log-layer in LES of full-depth Langmuir circulation. J. Fluid Mech. 699, 79–93.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. 117, C05001.10.1029/2011JC007516Google Scholar
Wu, J. 1973 Prediction of near-surface drift currents from wind velocity. J. Hydraul. Div. ASCE 99, 1291–1302.Google Scholar
Xuan, A. & Shen, L. 2019 A conservative scheme for simulation of free-surface turbulent and wave flows. J. Comput. Phys. 378, 18–43.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. 2011a Simulation of viscous flows with undulatory boundaries. Part I. Basic solver. J. Comput. Phys. 230, 5488–5509.Google Scholar
Yang, D. & Shen, L. 2011b Simulation of viscous flows with undulatory boundaries. Part II. Coupling with other solvers for two-fluid computations. J. Comput. Phys. 230, 5510–5531.10.1016/j.jcp.2011.02.035Google Scholar
Yang, Z., Deng, B. & Shen, L. 2018 Direct numerical simulation of wind turbulence over breaking waves. J. Fluid Mech. 850, 120–155.Google Scholar