Abstract
Wind-induced mixing forms the surface mixed layer (ML) above the stratified interior oceans. The ML depth (MLD), a key quantity for several upper ocean processes such as the air-sea interaction and primary production of phytoplankton biomass, is often scaled as \(U_{*}/\sqrt {Nf}\), where U∗ is the friction velocity, N is the Brunt-Väisälä frequency, and f is the Coriolis parameter. Here, we performed large-eddy simulations (LESs) to evaluate this scaling. It was found that the ML deepens rapidly until one-half inertial period (0.5Tf) by which the MLD becomes \(1.6 - 1.7 U_{*}/\sqrt {Nf}\). Thereafter, the ML deepening slows down but never stops, and the MLD keeps increasing gradually. The MLDs at Tf, 1.5Tf, and 5Tf become greater than those at 0.5Tf by 6.2 %, 16 %, and 40 %, respectively. Therefore, time-dependent scaling of the MLD is necessary for more quantitative estimates than the classical theory. LESs performed with several U∗, N, and f showed that the deepening rate of the ML depends on the Rossby number and the Froude number. The present study proposes time-dependent scalings of the ML deepening rate and the MLD as a function of the Rossby number and the Froude number, which cover the classical scaling but can be extended even after 0.5Tf.
Similar content being viewed by others
References
Belcher SE, Grant AL, Hanley KE, Fox-Kemper B, Van Roeke L, Sullivan PP, Large WG, Brown A, Hines A, Calvert D, Rutgersson A, Pettersson H, Bidlot JR, Janssen PA, Polton JA (2012) A global perspective on Langmuir turbulence in the ocean surface boundary layer. Geophys Res Lett 39 (17):1–9. https://doi.org/10.1029/2012GL052932
Bender MA, Ginis I, Kurihara Y (1993) Numerical simulations of tropical cyclone-ocean interaction with a high-resolution coupled model. J Geophys Res 98(D12):245–263. https://doi.org/10.1029/93jd02370
Botsford LW, Lawrence CA, Dever EP, Hastings A, Largier J (2006) Effects of variable winds on biological productivity on continental shelves in coastal upwelling systems. Deep-Sea Res II(53):3116–3140. https://doi.org/10.1016/j.dsr2.2006.07.011
Bulusu S, Rao KH, Srinivasa Rao N, Murty VSN, Sharp RJ (2002) Influence of a tropical cyclone on Chlorophyll-a Concentration in the Arabian Sea. Geophys Res Lett 29(22):22–1–22–4. https://doi.org/10.1029/2002gl015892
Davis C, Wang W, Chen SS, Chen Y, Corbosiero K, DeMaria M, Dudhia J, Holland G, Klemp J, Michalakes J, Reeves H, Rotunno R, Synder C, Xiao Q (2008) Prediction of landfalling hurricanes with the advanced hurricane WRF model. Mon Wea Rev 136(6):1990–2005. https://doi.org/10.1175/2007MWR2085.1
Deardorff J W (1980) Stratocumulus-capped mixed layers derived from a three-dimensional model. Bound-Layer Meteor 18(4):495–527. https://doi.org/10.1007/BF00119502
Emanuel K, DesAutels C, Holloway C, Korty R (2004) Environmental control of tropical cyclone intensity. J Atmos Sci 61(7):843–858. https://doi.org/10.1175/1520-0469(2004)061<0843:ECOTCI>2.0.CO;2
Ge X, Wang W, Kumar A, Zhang Y (2017) Importance of the vertical resolution in simulating SST diurnal and intraseasonal variability in an oceanic general circulation model. J Clim 30(11):3963–3978. https://doi.org/10.1175/JCLI-D-16-0689.1
Goh G, Noh Y (2013) Influence of the Coriolis force on the formation of a seasonal thermocline. Ocean Dyn 63(9-10):1083–1092. https://doi.org/10.1007/s10236-013-0645-x
Holtslag AAM, Boville BA (1993) Local versus nonlocal boundary-layer diffusion in a global climate model. J Clim 6(10):1825–1842. https://doi.org/10.1175/1520-0442(1993)006<1825:LVNBLD>2.0.CO;2
Huang CJ, Qiao F, Dai D (2014) Evaluating CMIP5 simulations of mixed layer depth during summer. J Geophys Res 119(4):2568–2582. https://doi.org/10.1002/2013JC009535
Kataoka T, Kimoto M, Watanabe M, Tatebe H (2019) Wind-mixed layer-SST feedbacks in a tropical air-sea coupled system: Application to the Atlantic. J Clim 32(13):3865–3881. https://doi.org/10.1175/JCLI-D-18-0728.1
Kiehl JT, Hack JJ, Hurrell JW (1998) The energy budget of the NCAR Community Climate Model: CCM3. J Clim 11(6):1151–1178. https://doi.org/10.1175/1520-0442(1998)011<1151:TEBOTN>2.0.CO;2
Large WG, Mcwilliams JC, Doney SC (1994) Oceanic vertical mixing - a review and a model with a nonlocal Boundary-Layer parameterization. Rev Geophys 32(94):363–403. https://doi.org/10.1029/94rg01872
Lozovatsky I, Figueroa M, Roget E, Fernando HJ, Shapovalov S (2005) Observations and scaling of the upper mixed layer in the North Atlantic. J Geophys Res 110(5):1–21. https://doi.org/10.1029/2004JC002708
Martinez E, Antoine D, D’Ortenzio F, De Boyer Montėgut C (2000) Phytoplankton spring and fall blooms in the North Atlantic in the 1980s and. J Geophys Res 116(11):1–11. https://doi.org/10.1029/2010JC006836
Niiler P, Kraus E (1977) One-dimensional models of the upper ocean. In: Modelling and prediction of the upper layers of the ocean, Pergamon, pp 143–172
Noh Y, Goh G, Raasch S (2010) Examination of the mixed layer deepening process during convection using LES. J Phys Oceanogr 40(9):2189–2195. https://doi.org/10.1175/2010JPO4277.1
Nolan DS, Zhang JA, Stern DP (2009) Evaluation of planetary boundary layer parameterizations in tropical cyclones by comparison of in situ observations and high-resolution simulations of Hurricane Isabel (2003). Part I: initialization, maximum winds, and the outer-core boundary layer. Mon Wea Rev 137(11):3651–3674. https://doi.org/10.1175/2009MWR2785.1
Obata A, Ishizaka J, Endoh M (1996) Global verification of critical depth theory for phytoplankton bloom with climatological in situ temperature and satellite ocean color data. J Geophys Res 101(C9):20657–20667. https://doi.org/10.1029/96JC01734
Pollard RT, Rhines PB, Thompson RORY (1973) The deepening of the Wind-Mixed layer. Geophys Fluid Dyn 4:381–404
Price JF, Ra W, Pinkel R (1986) Diurnal cycling: observations and models of the upper ocean response to diurnal heating, cooling, and wind mixing. J Geophys Res 91(C7):8411. https://doi.org/10.1029/JC091iC07p08411
Ushijima Y, Yoshikawa Y (2019) Mixed layer depth and sea surface warming under diurnally cycling surface heat flux in the heating season. J Phys Oceanogr 49(7):1769–1787. https://doi.org/10.1175/JPO-D-18-0230.1
Yoshikawa Y (2015) Scaling surface mixing/mixed layer depth under stabilizing buoyancy flux. J Phys Oceanogr 45(1):247–258. https://doi.org/10.1175/JPO-D-13-0190.1
Zilitinkevich SS, Baklanov A, Rost J, As Smedman, Lykosov V, Calanca P (2002a) Diagnostic and prognostic equations for the depth of the stably stratified Ekman boundary layer. Q J R Meteorol Soc 128:25–46. https://doi.org/10.1256/00359000260498770
Zilitinkevich SS, Perov VL, King JC (2002b) Near-surface turbulent fluxes in stable stratification: calculation techniques for use in general-circulation models. Q J R Meteorol Soc 128(583 PART A):1571–1587. https://doi.org/10.1256/00359000260247363
Zilitinkevich SS, Esau IN (2005) Resistance and heat-transfer laws for stable and neutral planetary boundary layers: old theory advanced and re-evaluated. Q J R Meteorol Soc 131(609):1863–1892. https://doi.org/10.1256/qj.04.143
Zilitinkevich SS, Esau I, Baklanov A (2007) Further comments on the equiliburium height of neutral and stable planetary boundary layer. Q J R Meteorol Soc 133(October):937–948. https://doi.org/10.1002/qj.27
Acknowledgements
Numerical computations were conducted using large-scale computer systems at the Cybermedia Center, Osaka University.
Funding
This work was financially supported by JSPS KAKENHI Grant Numbers JP15H05824.
Author information
Authors and Affiliations
Corresponding author
Additional information
Responsible Editor: Sandro Carniel
Data availability
The data used in this study are available online (https://fsv.iimc.kyoto-u.ac.jp/public/qkYIAAIcbQnAA1gBv4Zsx3CutotqQWym4HxQ6NhdK7aD).
Rights and permissions
About this article
Cite this article
Ushijima, Y., Yoshikawa, Y. Mixed layer deepening due to wind-induced shear-driven turbulence and scaling of the deepening rate in the stratified ocean. Ocean Dynamics 70, 505–512 (2020). https://doi.org/10.1007/s10236-020-01344-w
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10236-020-01344-w