Langmuir环流和波浪破碎对上层海洋混合影响的数值研究
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摘要
表面波主要通过两种方式影响上海洋混合层(OML)：(1)波浪破碎(WB),WB导致的波浪能量通量可以在海表提供额外湍动能源,同时增强近表层能量耗散；(2) Langmuir环流(LC),风生Stokes漂流与平均流共同作用导致的LC对OML内湍流生成和垂向混合的影响至关重要。尽管它们产生的湍流能量通量仅限于海表几米之内,但是它们却可以影响整个OML内的湍流混合过程。
混合层数值模拟,如,湍封闭模型已经被用于模拟OML (Kantha and Clayson,2004; Sun et al.2005),这些模型对于LC和其它混合过程的模拟研究尚不完整。本文利用MY2.5阶湍封闭模式,参照Craig和Banner (1994),通过修改边界条件及模式控制方程中的源函数项等,研究LC与其它动力和热力过程(WB、海表热通量)的相互作用机制,特别是WB和LC共同作用所引起的强混合问题。其中包括研究不同海况下(不同风速、不同破碎强度和不同海表热通量)LC对海洋上层混合(如：混合深度、强度、混合率等)的影响。通过逐一或联合考虑不同风速下、有无WB、不同海表热通量大小时,LC对海洋上层混合的影响。
为了更加细致地描述LC和WB对OML内湍流生成机制的相对作用,本文对介于直接数值模拟(DNS)和参数化湍封闭模式之间的三维湍流模拟工具—大涡模拟(LES)进行了改进,使之包含了OML中小尺度动力过程,并针对LC和WB对OML的影响进行数值模拟。通过分析湍动能收支,讨论了标准边界层(剪切和浮力)和考虑波浪影响下的湍流边界层(WB和LC)湍动能收支各项的相对重要性。另外,通过不同风速和不同波浪条件下的理想数值实验,考察了不同海况下LC和WB对混合机制的影响。
最后,利用LES方法模拟了伍兹霍尔实验室海气相互作用边界层耦合低风速观测实验(CBLAST-Low),并对湍流Langmuir数Lat大于2(剪切)、Lat,小于1(LC)、风速逐渐增强,风速逐渐减弱以及风速迅速减小五种情况下,比较分析了观测与LES数值实验结果间的异同,研究了LC和WB对湍流生成和混合机制的影响。
Surface waves affect the ocean surface mixed layer in two ways:(1) breaking waves inject turbulent kinetic energy at the ocean surface and create a near-surface layer of high energy dissipation; (2) the interaction of wave-induced Stokes drift current and mean wind-driven current generates counter-rotating vortices known as Langmuir circulations. Although both the turbulence energy flux due to breaking waves and the Stokes turbulence production are confined to the ocean surface within the top few meters, they can affect turbulent mixing processes throughout most of the ocean mixed layer.
Although mixed layer models such as turbulence closure model have been used to simulate OML (Kantha and Clayson,2004; Sun et al.2005), these models have not adequately quantified LC and other mixing processes. Like Craig and Banner (1994), a modified Mellor-Yamada 2.5 level turbulence closure model is used to parameterize LC and other mixing processes'effects on upper ocean mixing through changing boundary conditions and original equations. Numerical modeling study including how LC affects OML under different sea state (different wind speed, strength of WB and heat flux). Strong mixing processes by interaction between LC and WB are discussed particularly.
In order to describe the relative contributions of LC and WB to turbulence generation in OML, a three dimensional Large Eddy Simulation model (LES) is improved by including the small scale processes and used to investigate the effects of LC and WB on OML. By analyzing the turbulent kinetic energy (TKE) budget, the author examines the relative importance of standard boundary layer sources of TKE (shear and buoyancy production) to wave sources of TKE (LC and WB). This includes examination of the depths wave processes can influence. Furthermore, a number of cases under different wind and wave conditions have been conducted and the author assesses the relative importance of WB and LC in the mixed-layer dynamics as a function of sea state.
Finally, the author compares the LES model results with the turbulence measurements collected during the CBLAST-Low (Coupled Boundary layers and Air-sea Interaction-Low Winds) experiments by Woods Hole Oceanography Institute in five numerical experiments: turbulent Langmuir number Lat>2 (shear case), Lat<1 (LC case), increasing wind speed, decreasing wind speed and crazy down wind speed cases.
混合层数值模拟,如,湍封闭模型已经被用于模拟OML (Kantha and Clayson,2004; Sun et al.2005),这些模型对于LC和其它混合过程的模拟研究尚不完整。本文利用MY2.5阶湍封闭模式,参照Craig和Banner (1994),通过修改边界条件及模式控制方程中的源函数项等,研究LC与其它动力和热力过程(WB、海表热通量)的相互作用机制,特别是WB和LC共同作用所引起的强混合问题。其中包括研究不同海况下(不同风速、不同破碎强度和不同海表热通量)LC对海洋上层混合(如：混合深度、强度、混合率等)的影响。通过逐一或联合考虑不同风速下、有无WB、不同海表热通量大小时,LC对海洋上层混合的影响。
为了更加细致地描述LC和WB对OML内湍流生成机制的相对作用,本文对介于直接数值模拟(DNS)和参数化湍封闭模式之间的三维湍流模拟工具—大涡模拟(LES)进行了改进,使之包含了OML中小尺度动力过程,并针对LC和WB对OML的影响进行数值模拟。通过分析湍动能收支,讨论了标准边界层(剪切和浮力)和考虑波浪影响下的湍流边界层(WB和LC)湍动能收支各项的相对重要性。另外,通过不同风速和不同波浪条件下的理想数值实验,考察了不同海况下LC和WB对混合机制的影响。
最后,利用LES方法模拟了伍兹霍尔实验室海气相互作用边界层耦合低风速观测实验(CBLAST-Low),并对湍流Langmuir数Lat大于2(剪切)、Lat,小于1(LC)、风速逐渐增强,风速逐渐减弱以及风速迅速减小五种情况下,比较分析了观测与LES数值实验结果间的异同,研究了LC和WB对湍流生成和混合机制的影响。
Surface waves affect the ocean surface mixed layer in two ways:(1) breaking waves inject turbulent kinetic energy at the ocean surface and create a near-surface layer of high energy dissipation; (2) the interaction of wave-induced Stokes drift current and mean wind-driven current generates counter-rotating vortices known as Langmuir circulations. Although both the turbulence energy flux due to breaking waves and the Stokes turbulence production are confined to the ocean surface within the top few meters, they can affect turbulent mixing processes throughout most of the ocean mixed layer.
Although mixed layer models such as turbulence closure model have been used to simulate OML (Kantha and Clayson,2004; Sun et al.2005), these models have not adequately quantified LC and other mixing processes. Like Craig and Banner (1994), a modified Mellor-Yamada 2.5 level turbulence closure model is used to parameterize LC and other mixing processes'effects on upper ocean mixing through changing boundary conditions and original equations. Numerical modeling study including how LC affects OML under different sea state (different wind speed, strength of WB and heat flux). Strong mixing processes by interaction between LC and WB are discussed particularly.
In order to describe the relative contributions of LC and WB to turbulence generation in OML, a three dimensional Large Eddy Simulation model (LES) is improved by including the small scale processes and used to investigate the effects of LC and WB on OML. By analyzing the turbulent kinetic energy (TKE) budget, the author examines the relative importance of standard boundary layer sources of TKE (shear and buoyancy production) to wave sources of TKE (LC and WB). This includes examination of the depths wave processes can influence. Furthermore, a number of cases under different wind and wave conditions have been conducted and the author assesses the relative importance of WB and LC in the mixed-layer dynamics as a function of sea state.
Finally, the author compares the LES model results with the turbulence measurements collected during the CBLAST-Low (Coupled Boundary layers and Air-sea Interaction-Low Winds) experiments by Woods Hole Oceanography Institute in five numerical experiments: turbulent Langmuir number Lat>2 (shear case), Lat<1 (LC case), increasing wind speed, decreasing wind speed and crazy down wind speed cases.
引文
孙群,管长龙,宋金宝,波浪破碎对海洋上混合层内湍能量收支的影响,海洋与湖沼,2006,37(1),69-74
吴克俭,杨忠良,刘斌,管长龙,波浪对Ekman层的能量输入,中国科学D辑,2008,38(1),134-140
Agrawal, Y.C., E. A. Terray, M. A. Donelan, P. A. Hwan, A. J. Williams, W. M. Drennan, K. K. Kahma, and S. A. Kitaigorodskii. Enhanced dissipation of kinetic energy beneath surface waves. Nature,1992,359:219-220.
Araujo, M.,Denis Dartus, Philippe Maurel and Lucien Masbernat.,2001. Langmuir circulation and enhanced turbulence beneath wind-waves. Ocean Modelling.3,109-126.
Changlong guan, Wei Hu, Jian sun, and Ruili Li.2007. The whitecap coverage model from breaking dissipation parameterizations of wind waves. J. Geophys. Res.,112:C05031
Craig P D, Banner M L.1994. Modeling wave-enhanced turbulence in the ocean surface layer. J. Phys. Oceanogr.24:2546-2559
Craik A D D, Leibovich S.1976. A rational model for Langmuir circulations. J. Fluid Mech., 73:401-26
Craik A D D.1977. The generation of Langmuir circulation by an instability mechanism. J. Fluid Mech.,125:37-52
Dartus, D., Araujo, M., Maurel, P.H., Masbernat, L.,2000. On the influence of longitudinal mean flow over Langmuir circulations. Journal of Hydraulic Research 35,141-149.
Drennan, W.M., Kahma, K.K., Terray, E.A., Donelan, M.A., Kitaigorodskii, S.A.,1992. Observations of the enhancement of the kinetic energy dissipation beneath breaking wind waves. In:Banner, M.L., Grimshaw, R.H.J. (Eds.), Breaking Waves. Springer, pp.95-101.
Gemmrich JR, Banner ML, Garrett C.2008. Spectrally resolved energy dissipation rate and momentum flux of breaking waves. J. Phys. Oceanogr.38:1296-312
Gerbi PG, Trowbridge JH, Terry EA Plueddemann AJ, Kukulka T.2009. Observations of Turbulence in the Ocean Surface Boundary Layer:Energetic and Transport. J. Phys. Oceanogr.39:1077-1096.
Gnanadesikan, A.., Weller, R.A.,1995. Structure and stability of the Ekman spiral in the presence of surface gravity waves. J. Phys. Oceanogr.25,3148-3171.
Hasselmann K.,1970.Wave-driven inertial oscillations. Geophys. Fluid Dyn.,1,463-502.
Hsu C T, Hsu E Y, and Street R L.1981.On the structure of turbulent flow over a progressive water wave:Theory and experiment in a transformed wave-following coordinate system. J.Fluid Mech.,,105:87-117.
Hsu C T, Wu H W, Hsu E Y, Street R L.1982.Momentum and energy transfer in wind generation
of waves. J. Phys. Oceanogr.,,12:929-951.
Huang, N.E.,1971:Derivation of Stokes drift for a deep-water random gravity wave field. Deep-Sea Res.,18,255-259.
Kantha L H, Clayson A C.2004. On the effect of surface gravity waves on mixing in the oceanic mixed layer. Ocean Modelling.,101-124
Kenyon K.E.,1969. Stokes Drift for Random Gravity Waves. J. Geophys. Res.Vol,74,No.28,6991-6994.
Kitaigorodskii, S.A., M. A. Donelan, J. L. Lumley, and E. A. Terray,1983b.Wave-turbulence interactions in the upper ocean. Part II:Statistical characteristics of wave and turbulent components of the random velocity field in the marine surface layer. J. Phys. Oceanogr.,,13: 1988-1999
Kudryavtsev V N, Makin V K.2001.The impact of air-flow separation on the drag of the sea surface. Boundary-Layer Meteorology,,98:155-171.
Kukulka T, Hara T, Belcher S E.2007. A model of the air-sea momentum flux and breaking-wave distribution for strongly forced wind waves. J. Phys. Oceanogr.,37(7):1811-1828.
Kraus E B, Turner J S.1967. A one-dimensional model of the seasonal thermocline:Ⅱ. The general Theory and its consequences. Tellus,19:98-105
Lane EM, Restrepo JM, McWilliams JC.2007. Wave-current interaction:a comparison of radiation-stress and vortex-force representations. J. Phys. Oceanogr.37:1122-41
Langmuir I.,1938. Surface motion of water induced by wind. Science.87,119-123.
Leibovich S.1983. The form and dynamics of Langmuir circulation, Ann. Rev. Fluid Mech.,15: 391-427
Leibovich S.1977. Convective instability of stably stratified water in the ocean. J. Fluid Mech.,82:561-591
Lewis, D. M., and S. E. Belcher,2004:Time-dependent, coupled, Ekman boundary layer solutions incorporating Stokes drift. Dyn. Atmos. Oceans,37,313-351.
Li, M. and C. Garrett,1993:Cell merging and the jet/downwelling ratio in Langmuir circulation. J.Mar. Res.,51,737-769.
Li, M. and C. Garrett,1995:Is Langmuir circulation driven by surface waves or surface cooling? J. Phys. Oceanogr.,25,64-76.
Li, M. and C. Garrett,1997:Mixed-layer deepening due to Langmuir circulation. J. Phys Oceanogr.,27,121-132.
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.
Li Shuang, Song Jin bao, Sun Qun,.2008. Effect of Stokes drift on upper ocean mixing. Acta Oceanologica Sinica. Vol.28, No.2, P.1-10(SCI)
Madsen, O. S.,1978:Mass transport in deep-water waves. J. Phys. Oceanogr.,8,1009-1015.
Maurel, Ph., Araujo, M., Dartus, D., Masbernat, L., Terrisse, f.,1997. Upper mixed layer dynamics under wind-waves. Journal de Recherche Oceanographique 22,53-59.
Mcwillianms J C, Sullivan P P, Moeng C H.1997. Langmuir turbulence in the ocean. J. Fluid Mech.,334:1-30
Mcwillianms J C and Restrepo J.M.,1999. The Wave-Driven Ocean Criculation. J. Phys. Oceanogr.,29,2523-2540.
Mellor G L, Yamada T.1974. A hierarchy of turbulence closure model for Planetary boundary layers. J. Atmos. Sci.,31:1791-1806
Mellor G L, Yamada T.1982. Development of a turbulence closure model for geophysical fluid problems. Rev. Geophys. Space Phys.,20:851-875
Mellor G L.2003. The Three-Dimensional Current and Surface Wave Equations. J. Phys. Oceanogr.,33,1978-1989.
Melville W K.1996.The role of surface-wave breaking in air-sea interaction. Annu. Rev. Fluid Mech.,,26:279-321.
Melville W K, Matusov P.2002. Distribution of breaking waves at the ocean surface. Nature,, 417:58-63.
Melville W K, Veron F, White C J.2002.The velocity field under breaking waves:coherent structures and turbulence. J. Fluid Mech.,,454:203-233.
Mitsuyasu H.1985. A note on the momentum transfer from wind to waves. J. Geophys. Res.,, 90:3343-3345.
Mizuno,S.,1985. Langmuir circulation in a laboratory tank. Report of the Institute for Applied Mechanixs 31,47-59.
Noh Y,Min HS, Raasch S.2004. Large eddy simulation of the ocean mixed layer:the effects of wave breaking and Langmuir circulation. J. Phys. Oceanogr.34:720-35
Polton,J.A., D.M.Lewis and S.E. Belcher,2005. The role of wave-induced Coriolis-Stokes forcing on the wind-driven mixed layer. J. Phys. Oceanogr.,35,444-457.
Pierson W J, L Moskowits.1964. A proposed spectral form for fully developed wind seas based in the similarity theory of S. A. Kitaigorodskii. J. Geophys. Res.,69:5181-5190
Qiao F, Yuan Y, Yang Y, Zheng Q, Xia C, Ma J.2004.Wave-induced mixing in the upper ocean:Distribution and application to a global ocean circulation model. Geophy. Res. Lett., 31:L11303.
Rapp R J, Melville W K.1990. Laboratory measurements of deep water breaking waves. Philos.Trans. Roy. Soc. London,, A331:735-800.
Sun Qun, Song Jinbao, Guan Changlong.,2005. Simulation of the ocean surface mixed layer under the wave breaking. Acta Oceanologica Sinica,24(3):9-15
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-oceans,100(c5):8501-8522
Terray EA, Donelan MA, Agrawal YC, Drennan WM, Kahma KK, Williams III AJ, Hwang PA, Kitaigorodskii SA.1996, Estimates of kinetic energy dissipation under breaking waves. J. Phys.Oceanogr.,26:792-807.
Teixeira, M. A. C., and S. E. Belcher,2002:On the distortion of turbulence by a progressive surface wave. J. Fluid Mech.,458,229-267.
Thorpe SA, Osborn TR, Farmer DM, et al.,2003. Bubble clouds and Langmuir circulation: Observations and models. J. Phys. Oceanogr.33 (9):2013-2031.
Thorpe, S.A.,2004. Langmuir Circulation.Annu.Rev.Fluid Mech.36,55-79.
Wang W, Huang R X.2004, Wind energy input to the Ekman layer. J. Phys. Oceanogr., 34(5):1267-1275.
Zhang S W, Yuan Y L.2005, Energy and momentum dissipation through wave breaking. J.Geophys. Res.,110:C09021.
Zhang S W, Yuan Y L, Zheng Q A.2007, Modeling of the eddy viscosity by breaking waves. Acta Oceanologica Sinica,26(6):116-123.
Zhao D L, Lou A G 2003, New interpretation of dependence of wind stress on wave state. China Ocean Engineering,17(4):577-588.
吴克俭,杨忠良,刘斌,管长龙,波浪对Ekman层的能量输入,中国科学D辑,2008,38(1),134-140
Agrawal, Y.C., E. A. Terray, M. A. Donelan, P. A. Hwan, A. J. Williams, W. M. Drennan, K. K. Kahma, and S. A. Kitaigorodskii. Enhanced dissipation of kinetic energy beneath surface waves. Nature,1992,359:219-220.
Araujo, M.,Denis Dartus, Philippe Maurel and Lucien Masbernat.,2001. Langmuir circulation and enhanced turbulence beneath wind-waves. Ocean Modelling.3,109-126.
Changlong guan, Wei Hu, Jian sun, and Ruili Li.2007. The whitecap coverage model from breaking dissipation parameterizations of wind waves. J. Geophys. Res.,112:C05031
Craig P D, Banner M L.1994. Modeling wave-enhanced turbulence in the ocean surface layer. J. Phys. Oceanogr.24:2546-2559
Craik A D D, Leibovich S.1976. A rational model for Langmuir circulations. J. Fluid Mech., 73:401-26
Craik A D D.1977. The generation of Langmuir circulation by an instability mechanism. J. Fluid Mech.,125:37-52
Dartus, D., Araujo, M., Maurel, P.H., Masbernat, L.,2000. On the influence of longitudinal mean flow over Langmuir circulations. Journal of Hydraulic Research 35,141-149.
Drennan, W.M., Kahma, K.K., Terray, E.A., Donelan, M.A., Kitaigorodskii, S.A.,1992. Observations of the enhancement of the kinetic energy dissipation beneath breaking wind waves. In:Banner, M.L., Grimshaw, R.H.J. (Eds.), Breaking Waves. Springer, pp.95-101.
Gemmrich JR, Banner ML, Garrett C.2008. Spectrally resolved energy dissipation rate and momentum flux of breaking waves. J. Phys. Oceanogr.38:1296-312
Gerbi PG, Trowbridge JH, Terry EA Plueddemann AJ, Kukulka T.2009. Observations of Turbulence in the Ocean Surface Boundary Layer:Energetic and Transport. J. Phys. Oceanogr.39:1077-1096.
Gnanadesikan, A.., Weller, R.A.,1995. Structure and stability of the Ekman spiral in the presence of surface gravity waves. J. Phys. Oceanogr.25,3148-3171.
Hasselmann K.,1970.Wave-driven inertial oscillations. Geophys. Fluid Dyn.,1,463-502.
Hsu C T, Hsu E Y, and Street R L.1981.On the structure of turbulent flow over a progressive water wave:Theory and experiment in a transformed wave-following coordinate system. J.Fluid Mech.,,105:87-117.
Hsu C T, Wu H W, Hsu E Y, Street R L.1982.Momentum and energy transfer in wind generation
of waves. J. Phys. Oceanogr.,,12:929-951.
Huang, N.E.,1971:Derivation of Stokes drift for a deep-water random gravity wave field. Deep-Sea Res.,18,255-259.
Kantha L H, Clayson A C.2004. On the effect of surface gravity waves on mixing in the oceanic mixed layer. Ocean Modelling.,101-124
Kenyon K.E.,1969. Stokes Drift for Random Gravity Waves. J. Geophys. Res.Vol,74,No.28,6991-6994.
Kitaigorodskii, S.A., M. A. Donelan, J. L. Lumley, and E. A. Terray,1983b.Wave-turbulence interactions in the upper ocean. Part II:Statistical characteristics of wave and turbulent components of the random velocity field in the marine surface layer. J. Phys. Oceanogr.,,13: 1988-1999
Kudryavtsev V N, Makin V K.2001.The impact of air-flow separation on the drag of the sea surface. Boundary-Layer Meteorology,,98:155-171.
Kukulka T, Hara T, Belcher S E.2007. A model of the air-sea momentum flux and breaking-wave distribution for strongly forced wind waves. J. Phys. Oceanogr.,37(7):1811-1828.
Kraus E B, Turner J S.1967. A one-dimensional model of the seasonal thermocline:Ⅱ. The general Theory and its consequences. Tellus,19:98-105
Lane EM, Restrepo JM, McWilliams JC.2007. Wave-current interaction:a comparison of radiation-stress and vortex-force representations. J. Phys. Oceanogr.37:1122-41
Langmuir I.,1938. Surface motion of water induced by wind. Science.87,119-123.
Leibovich S.1983. The form and dynamics of Langmuir circulation, Ann. Rev. Fluid Mech.,15: 391-427
Leibovich S.1977. Convective instability of stably stratified water in the ocean. J. Fluid Mech.,82:561-591
Lewis, D. M., and S. E. Belcher,2004:Time-dependent, coupled, Ekman boundary layer solutions incorporating Stokes drift. Dyn. Atmos. Oceans,37,313-351.
Li, M. and C. Garrett,1993:Cell merging and the jet/downwelling ratio in Langmuir circulation. J.Mar. Res.,51,737-769.
Li, M. and C. Garrett,1995:Is Langmuir circulation driven by surface waves or surface cooling? J. Phys. Oceanogr.,25,64-76.
Li, M. and C. Garrett,1997:Mixed-layer deepening due to Langmuir circulation. J. Phys Oceanogr.,27,121-132.
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.
Li Shuang, Song Jin bao, Sun Qun,.2008. Effect of Stokes drift on upper ocean mixing. Acta Oceanologica Sinica. Vol.28, No.2, P.1-10(SCI)
Madsen, O. S.,1978:Mass transport in deep-water waves. J. Phys. Oceanogr.,8,1009-1015.
Maurel, Ph., Araujo, M., Dartus, D., Masbernat, L., Terrisse, f.,1997. Upper mixed layer dynamics under wind-waves. Journal de Recherche Oceanographique 22,53-59.
Mcwillianms J C, Sullivan P P, Moeng C H.1997. Langmuir turbulence in the ocean. J. Fluid Mech.,334:1-30
Mcwillianms J C and Restrepo J.M.,1999. The Wave-Driven Ocean Criculation. J. Phys. Oceanogr.,29,2523-2540.
Mellor G L, Yamada T.1974. A hierarchy of turbulence closure model for Planetary boundary layers. J. Atmos. Sci.,31:1791-1806
Mellor G L, Yamada T.1982. Development of a turbulence closure model for geophysical fluid problems. Rev. Geophys. Space Phys.,20:851-875
Mellor G L.2003. The Three-Dimensional Current and Surface Wave Equations. J. Phys. Oceanogr.,33,1978-1989.
Melville W K.1996.The role of surface-wave breaking in air-sea interaction. Annu. Rev. Fluid Mech.,,26:279-321.
Melville W K, Matusov P.2002. Distribution of breaking waves at the ocean surface. Nature,, 417:58-63.
Melville W K, Veron F, White C J.2002.The velocity field under breaking waves:coherent structures and turbulence. J. Fluid Mech.,,454:203-233.
Mitsuyasu H.1985. A note on the momentum transfer from wind to waves. J. Geophys. Res.,, 90:3343-3345.
Mizuno,S.,1985. Langmuir circulation in a laboratory tank. Report of the Institute for Applied Mechanixs 31,47-59.
Noh Y,Min HS, Raasch S.2004. Large eddy simulation of the ocean mixed layer:the effects of wave breaking and Langmuir circulation. J. Phys. Oceanogr.34:720-35
Polton,J.A., D.M.Lewis and S.E. Belcher,2005. The role of wave-induced Coriolis-Stokes forcing on the wind-driven mixed layer. J. Phys. Oceanogr.,35,444-457.
Pierson W J, L Moskowits.1964. A proposed spectral form for fully developed wind seas based in the similarity theory of S. A. Kitaigorodskii. J. Geophys. Res.,69:5181-5190
Qiao F, Yuan Y, Yang Y, Zheng Q, Xia C, Ma J.2004.Wave-induced mixing in the upper ocean:Distribution and application to a global ocean circulation model. Geophy. Res. Lett., 31:L11303.
Rapp R J, Melville W K.1990. Laboratory measurements of deep water breaking waves. Philos.Trans. Roy. Soc. London,, A331:735-800.
Sun Qun, Song Jinbao, Guan Changlong.,2005. Simulation of the ocean surface mixed layer under the wave breaking. Acta Oceanologica Sinica,24(3):9-15
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-oceans,100(c5):8501-8522
Terray EA, Donelan MA, Agrawal YC, Drennan WM, Kahma KK, Williams III AJ, Hwang PA, Kitaigorodskii SA.1996, Estimates of kinetic energy dissipation under breaking waves. J. Phys.Oceanogr.,26:792-807.
Teixeira, M. A. C., and S. E. Belcher,2002:On the distortion of turbulence by a progressive surface wave. J. Fluid Mech.,458,229-267.
Thorpe SA, Osborn TR, Farmer DM, et al.,2003. Bubble clouds and Langmuir circulation: Observations and models. J. Phys. Oceanogr.33 (9):2013-2031.
Thorpe, S.A.,2004. Langmuir Circulation.Annu.Rev.Fluid Mech.36,55-79.
Wang W, Huang R X.2004, Wind energy input to the Ekman layer. J. Phys. Oceanogr., 34(5):1267-1275.
Zhang S W, Yuan Y L.2005, Energy and momentum dissipation through wave breaking. J.Geophys. Res.,110:C09021.
Zhang S W, Yuan Y L, Zheng Q A.2007, Modeling of the eddy viscosity by breaking waves. Acta Oceanologica Sinica,26(6):116-123.
Zhao D L, Lou A G 2003, New interpretation of dependence of wind stress on wave state. China Ocean Engineering,17(4):577-588.