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that most of the Langmuir-turbulence-induced variations of are explained by a dependence on the Langmuir number, and this effect is additive rather than multiplicative to the convective turbulence-induced variations. Indeed, Langmuir turbulence and convective turbulence share some similarities in enhancing the vertical mixing. Namely, the intermittent downwelling jets associated with the Langmuir circulation ( Polton and Belcher 2007 ) driven by the Stokes shear force ( Suzuki and Fox-Kemper 2016
that most of the Langmuir-turbulence-induced variations of are explained by a dependence on the Langmuir number, and this effect is additive rather than multiplicative to the convective turbulence-induced variations. Indeed, Langmuir turbulence and convective turbulence share some similarities in enhancing the vertical mixing. Namely, the intermittent downwelling jets associated with the Langmuir circulation ( Polton and Belcher 2007 ) driven by the Stokes shear force ( Suzuki and Fox-Kemper 2016
.1029/2018GL080296 . 10.1029/2018GL080296 Craik , A. D. D. , and S. Leibovich , 1976 : A rational model for Langmuir circulations . J. Fluid Mech. , 73 , 401 – 426 , https://doi.org/10.1017/S0022112076001420 . 10.1017/S0022112076001420 D’Asaro , E. A. , 2014 : Turbulence in the upper-ocean mixed layer . Annu. Rev. Mar. Sci. , 6 , 101 – 115 , https://doi.org/10.1146/annurev-marine-010213-135138 . 10.1146/annurev-marine-010213-135138 Denman , K. L. , and A. E. Gargett , 1995
.1029/2018GL080296 . 10.1029/2018GL080296 Craik , A. D. D. , and S. Leibovich , 1976 : A rational model for Langmuir circulations . J. Fluid Mech. , 73 , 401 – 426 , https://doi.org/10.1017/S0022112076001420 . 10.1017/S0022112076001420 D’Asaro , E. A. , 2014 : Turbulence in the upper-ocean mixed layer . Annu. Rev. Mar. Sci. , 6 , 101 – 115 , https://doi.org/10.1146/annurev-marine-010213-135138 . 10.1146/annurev-marine-010213-135138 Denman , K. L. , and A. E. Gargett , 1995
mechanism of wave-enhanced turbulence affecting regions farther from the boundary has been proposed. The shear in surface-wave Stokes drift is hypothesized to rotate existing vertical vorticity (potentially seeded by wave breaking) into streamwise vorticity ( Craik and Leibovich 1976 ). The resulting Langmuir circulations are often visually striking ( Langmuir 1938 ). Coherent turbulent structures manifest as wave-aligned rows of bubbles (or other buoyant particulates), which gather in convergence zones
mechanism of wave-enhanced turbulence affecting regions farther from the boundary has been proposed. The shear in surface-wave Stokes drift is hypothesized to rotate existing vertical vorticity (potentially seeded by wave breaking) into streamwise vorticity ( Craik and Leibovich 1976 ). The resulting Langmuir circulations are often visually striking ( Langmuir 1938 ). Coherent turbulent structures manifest as wave-aligned rows of bubbles (or other buoyant particulates), which gather in convergence zones
the Ocean . Elsevier , 602 pp. Leibovich , S. , 1983 : The form and dynamics of Langmuir circulations . Annu. Rev. Fluid Mech. , 15 , 391 – 427 , https://doi.org/10.1146/annurev.fl.15.010183.002135 . 10.1146/annurev.fl.15.010183.002135 Li , Q. , A. Webb , B. Fox-Kemper , A. Craig , G. Danabasoglu , W. G. Large , and M. Vertenstein , 2016 : Langmuir mixing effects on global climate: WAVEWATCH III in CESM . Ocean Modell. , 103 , 145 – 160 , https://doi.org/10
the Ocean . Elsevier , 602 pp. Leibovich , S. , 1983 : The form and dynamics of Langmuir circulations . Annu. Rev. Fluid Mech. , 15 , 391 – 427 , https://doi.org/10.1146/annurev.fl.15.010183.002135 . 10.1146/annurev.fl.15.010183.002135 Li , Q. , A. Webb , B. Fox-Kemper , A. Craig , G. Danabasoglu , W. G. Large , and M. Vertenstein , 2016 : Langmuir mixing effects on global climate: WAVEWATCH III in CESM . Ocean Modell. , 103 , 145 – 160 , https://doi.org/10
: A rational model for Langmuir circulation . J. Fluid Mech. , 73 , 401 – 426 , https://doi.org/10.1017/S0022112076001420 . 10.1017/S0022112076001420 Fujiwara , Y. , Y. Yoshikawa , and Y. Matsumura , 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 , 1691 – 1708 , https://doi.org/10.1175/JPO-D-17-0199.1 . 10
: A rational model for Langmuir circulation . J. Fluid Mech. , 73 , 401 – 426 , https://doi.org/10.1017/S0022112076001420 . 10.1017/S0022112076001420 Fujiwara , Y. , Y. Yoshikawa , and Y. Matsumura , 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 , 1691 – 1708 , https://doi.org/10.1175/JPO-D-17-0199.1 . 10
Noh and Choi (2018 , hereinafter NC ) recently submitted a comment on the published work of Pearson et al. (2015 , hereinafter PGPB ). In their comment, Noh and Choi suggest that the depth of the thermocline should be scaled by the Zilitinkevich scale L Z ( Zilitinkevich 1972 ), as opposed to PGPB who suggested that the mixed and boundary layer depths scale as a combination of the Langmuir stability length L L ( Belcher et al. 2012 ) and initial ocean surface boundary layer (OSBL
Noh and Choi (2018 , hereinafter NC ) recently submitted a comment on the published work of Pearson et al. (2015 , hereinafter PGPB ). In their comment, Noh and Choi suggest that the depth of the thermocline should be scaled by the Zilitinkevich scale L Z ( Zilitinkevich 1972 ), as opposed to PGPB who suggested that the mixed and boundary layer depths scale as a combination of the Langmuir stability length L L ( Belcher et al. 2012 ) and initial ocean surface boundary layer (OSBL
determine the inertial currents in the OSBL, and the evolution of the mixed layer depth. The model is described in appendix B . The thickness of OSBL is assumed to increase through entrainment, with two parameterizations of entrainment considered. The first assumes that entrainment is driven by a combination of convective and Langmuir turbulence (this will be referred to as the Langmuir model). Parameterization of entrainment due to Langmuir turbulence have been proposed by Grant and Belcher (2009
determine the inertial currents in the OSBL, and the evolution of the mixed layer depth. The model is described in appendix B . The thickness of OSBL is assumed to increase through entrainment, with two parameterizations of entrainment considered. The first assumes that entrainment is driven by a combination of convective and Langmuir turbulence (this will be referred to as the Langmuir model). Parameterization of entrainment due to Langmuir turbulence have been proposed by Grant and Belcher (2009
1. Introduction Interaction between Stokes drift velocity generated by surface gravity waves and the wind-driven shear current gives rise to Langmuir turbulence in the upper ocean, characterized by Langmuir circulation (LC) across a wide range of spatial and temporal scales. LC consists of parallel counterrotating vortices aligned in the direction of the wind ranging in scale from centimeters to kilometers in the downwind direction. The largest of the LC scales can extend down to the base of
1. Introduction Interaction between Stokes drift velocity generated by surface gravity waves and the wind-driven shear current gives rise to Langmuir turbulence in the upper ocean, characterized by Langmuir circulation (LC) across a wide range of spatial and temporal scales. LC consists of parallel counterrotating vortices aligned in the direction of the wind ranging in scale from centimeters to kilometers in the downwind direction. The largest of the LC scales can extend down to the base of
meter~ in the mixing layer beneath a freely drifting spar buoyshowed that the buoy must bc in a convergence zone, where transport of warm water downwards enhances thediurnal heating effect. The convergence zone is probably associated with Langmuir circulations due to thestrong, steady wind experienced before and during the 6-day deployment. This paper describes a two-dimensional numerical model of a Langmuir cell imposed on a mixed layer. Theprocesses of advecfion and mixing occur separately at
meter~ in the mixing layer beneath a freely drifting spar buoyshowed that the buoy must bc in a convergence zone, where transport of warm water downwards enhances thediurnal heating effect. The convergence zone is probably associated with Langmuir circulations due to thestrong, steady wind experienced before and during the 6-day deployment. This paper describes a two-dimensional numerical model of a Langmuir cell imposed on a mixed layer. Theprocesses of advecfion and mixing occur separately at
column depth . It is believed that winds generate turbulence in the upper ocean both through direct action of wind stress on the surface and through an indirect process involving surface waves. A term in the wave-averaged momentum equation incorporating the latter mechanism, first derived by Craik and Leibovich (1976) , will be here termed the Langmuir vortex force to clearly identify the process represented as that leading to Langmuir circulations (LC; Langmuir 1938 ). Both effects of wind
column depth . It is believed that winds generate turbulence in the upper ocean both through direct action of wind stress on the surface and through an indirect process involving surface waves. A term in the wave-averaged momentum equation incorporating the latter mechanism, first derived by Craik and Leibovich (1976) , will be here termed the Langmuir vortex force to clearly identify the process represented as that leading to Langmuir circulations (LC; Langmuir 1938 ). Both effects of wind
