Turbulence modeling in ocean circulation problems
A physical formulation of the problem is considered. A mathematical model and a numerical algorithm of the turbulence model as part of the ocean circulation model for simulations for decades are formulated. The model is based on the evolution equations for turbulent kinetic energy (TKE) and the freq...
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| Published in | Izvestiya. Atmospheric and oceanic physics Vol. 50; no. 1; pp. 49 - 60 |
|---|---|
| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
Moscow
Pleiades Publishing
01.01.2014
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0001-4338 1555-628X |
| DOI | 10.1134/S0001433813060121 |
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| Abstract | A physical formulation of the problem is considered. A mathematical model and a numerical algorithm of the turbulence model as part of the ocean circulation model for simulations for decades are formulated. The model is based on the evolution equations for turbulent kinetic energy (TKE) and the frequency of its viscous dissipation. A numerical solution algorithm for both the circulation model and the turbulence model is based on implicit schemes of splitting with respect to physical processes and geometric coordinates. For the turbulence model, this provided analytical solutions at a splitting step related to TKE generation and dissipation. Numerical experiments have been performed with a model of the joint circulation of the North Atlantic, the Arctic Ocean, and the Bering Sea to reproduce the annual cycle and synoptic disturbances of ocean characteristics. The model has a resolution of 0.25° in latitude and longitude and 40 levels in the vertical, which are compressed toward the surface to reproduce the process of developed turbulence better. The results are compared with observations and with the results of simulations using traditional parameterizations of the upper ocean mixing. It is shown that the model reproduces ocean characteristics correctly, only slightly increasing the computation time in comparison with simple parameterizations. Spatial and temporal characteristics of turbulence are analyzed. |
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| AbstractList | A physical formulation of the problem is considered. A mathematical model and a numerical algorithm of the turbulence model as part of the ocean circulation model for simulations for decades are formulated. The model is based on the evolution equations for turbulent kinetic energy (TKE) and the frequency of its viscous dissipation. A numerical solution algorithm for both the circulation model and the turbulence model is based on implicit schemes of splitting with respect to physical processes and geometric coordinates. For the turbulence model, this provided analytical solutions at a splitting step related to TKE generation and dissipation. Numerical experiments have been performed with a model of the joint circulation of the North Atlantic, the Arctic Ocean, and the Bering Sea to reproduce the annual cycle and synoptic disturbances of ocean characteristics. The model has a resolution of 0.25 degree in latitude and longitude and 40 levels in the vertical, which are compressed toward the surface to reproduce the process of developed turbulence better. The results are compared with observations and with the results of simulations using traditional parameterizations of the upper ocean mixing. It is shown that the model reproduces ocean characteristics correctly, only slightly increasing the computation time in comparison with simple parameterizations. Spatial and temporal characteristics of turbulence are analyzed. A physical formulation of the problem is considered. A mathematical model and a numerical algorithm of the turbulence model as part of the ocean circulation model for simulations for decades are formulated. The model is based on the evolution equations for turbulent kinetic energy (TKE) and the frequency of its viscous dissipation. A numerical solution algorithm for both the circulation model and the turbulence model is based on implicit schemes of splitting with respect to physical processes and geometric coordinates. For the turbulence model, this provided analytical solutions at a splitting step related to TKE generation and dissipation. Numerical experiments have been performed with a model of the joint circulation of the North Atlantic, the Arctic Ocean, and the Bering Sea to reproduce the annual cycle and synoptic disturbances of ocean characteristics. The model has a resolution of 0.25° in latitude and longitude and 40 levels in the vertical, which are compressed toward the surface to reproduce the process of developed turbulence better. The results are compared with observations and with the results of simulations using traditional parameterizations of the upper ocean mixing. It is shown that the model reproduces ocean characteristics correctly, only slightly increasing the computation time in comparison with simple parameterizations. Spatial and temporal characteristics of turbulence are analyzed. A physical formulation of the problem is considered. A mathematical model and a numerical algorithm of the turbulence model as part of the ocean circulation model for simulations for decades are formulated. The model is based on the evolution equations for turbulent kinetic energy (TKE) and the frequency of its viscous dissipation. A numerical solution algorithm for both the circulation model and the turbulence model is based on implicit schemes of splitting with respect to physical processes and geometric coordinates. For the turbulence model, this provided analytical solutions at a splitting step related to TKE generation and dissipation. Numerical experiments have been performed with a model of the joint circulation of the North Atlantic, the Arctic Ocean, and the Bering Sea to reproduce the annual cycle and synoptic disturbances of ocean characteristics. The model has a resolution of 0.25° in latitude and longitude and 40 levels in the vertical, which are compressed toward the surface to reproduce the process of developed turbulence better. The results are compared with observations and with the results of simulations using traditional parameterizations of the upper ocean mixing. It is shown that the model reproduces ocean characteristics correctly, only slightly increasing the computation time in comparison with simple parameterizations. Spatial and temporal characteristics of turbulence are analyzed.[PUBLICATION ABSTRACT] |
| Author | Gusev, A. V. Tamsalu, R. Moshonkin, S. N. Zalesny, V. B. |
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| Cites_doi | 10.1134/S0001437006020020 10.1175/1520-0469(1988)045<0055:AQETEM>2.0.CO;2 10.1029/97JC01585 10.1515/rjnamm.2011.009 10.1515/rjnamm.2010.036 10.1134/S0001433810060034 10.1098/rspa.1970.0125 10.1017/CBO9780511801198 10.1175/1520-0485(2002)032<0240:OTPIVD>2.0.CO;2 10.1029/94RG01872 10.1175/1520-0442(2001)014<2079:PAGOHW>2.0.CO;2 10.1175/1520-0485(2001)031<1413:OTPIOP>2.0.CO;2 10.1134/S000143700706001X 10.1029/JC082i012p01735 10.1029/RG020i004p00851 10.1016/j.ocemod.2003.12.003 10.1016/S1463-5003(00)00014-7 |
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Oceanogr.19811114421451 MoshonkinS NEstimates of turbulence coefficients for the ocean circulation modelComputational Mathematics and Mathematical Modeling2000MoscowINM RAS ZalesnyV BMarchukG IAgoshkovV IBagnoA VGusevA VDianskyN AMoshonkinS NTamsaluRVolodinE MNumerical modeling of large-scale ocean circulation based on the multicomponent splitting methodRuss. J. Numer. Anal. Math. Modelling201025658160910.1515/rjnamm.2010.036 SuffmanP GA model for inhomogeneous turbulent flowProc. R. Soc., Lond. A197031741743310.1098/rspa.1970.0125 MaslovskiWKinneyJ CMarbleDTowards Eddy-Resolving Models of Arctic Ocean. Ocean Modelling in an Eddying Regime. Geophysical Monograph Series 177. 10.1029/177GM162008 MunkW HAndersonE RNotes on a theory of the thermoclineJ. Mar. Res.194873276295 CanutoV MHowardAChengYDubovikovM SOcean turbulence I: One-point closure model. Momentum and heat vertical diffusivitiesJ. Phys. Oceanogr.20013161413142610.1175/1520-0485(2001)031<1413:OTPIOP>2.0.CO;2 KolmogorovA NEquations of turbulent motion of incompressible fluidIzv. Akad. Nauk SSSR: Ser. Fiz.1942615568 MarchukG IMethods of Computational Mathematics1980MoscowNauka ZalesnyV BGusevA VMathematical model of the World ocean dynamics with temperature and salinity variational data assimilation algorithmsRuss. J. Numer. Anal. Math. Modeling2009242171191 HowardAChengYDubovikovM SOcean turbulence. Part II: Vertical diffusivities of momentum, heat, salt, mass, and passive scalarsJ. Phys. Oceanogr.200232124026410.1175/1520-0485(2002)032<0240:OTPIVD>2.0.CO;2 BurchardHBoldingKVillarrealM RGOTM, a General Ocean Turbulence Model. Theory, Implementation and Test Case, EUR 187451999 SteeleMMorleyRErmoldWPHC: A global ocean hydrography with a high-quality Arctic OceanJ. Clim.20011492079208710.1175/1520-0442(2001)014<2079:PAGOHW>2.0.CO;2 LargeW GMcWilliamsJ CDoneyS COceanic vertical mixing: a review and a model with a nonlocal boundary layer parameterizationRev. Geophys.19943236340310.1029/94RG01872 KocherginV PKlimokV ISukhorukovV AThe homogeneous layer of the ocean within “differential” modelsNumerical Methods of Continuum Mechanics1977NovosibirskComputing Center of SR RAS102114 GriffiesS MBoningCBryanF OChassignetE PGerdesRHasumiHHirstATreguierA-MWebbDDevelopments in ocean climate modelingOcean Modelling2000212319210.1016/S1463-5003(00)00014-7 DianskyN ABagnoA VZalesnyV BSigma model of global ocean circulation and its sensitivity to variations in wind stressIzv., Atmos. Ocean. Phys.2002384477494 LargeW GYagerS GDiurnal to Decadal Global Forcing for Ocean and Sea-Ice Models: The Data Sets and Flux Climatologies2004Boulder, ColoradoClimate and Global Dynamics Division, National Center for Atmospheric Research ZaslavskiiM MZalesnyV BKabatchenkoI MTamsaluR OOn the self-adjusted description of the atmospheric boundary layer, wind waves, and sea currentsOceanology200646215916910.1134/S0001437006020020 KrausE BModelling and Prediction of the Upper Layers of the Ocean1977 MarchukG ISplitting Methods1988MoscowNauka MoninA SOzmidovR VOceanic Turbulence1981LeningradGidrometeoizdat GalperinBKanthaLHHassidSRosatiAA quasi-equilibrium turbulent energy model for geophysical flowsJ. Atmos. Sci.198845556210.1175/1520-0469(1988)045<0055:AQETEM>2.0.CO;2 WarnerJ CSherwoodC RArangoH GSignellR PPerformance of four turbulence closure models implemented using a generic length scale methodOcean Modelling200581–28111310.1016/j.ocemod.2003.12.003 MoshonkinS NTamsaluRZalesnyV BModeling sea dynamics and turbulent zones on high spatial resolution nested gridsOceanology200747674775710.1134/S000143700706001X GarternichtUSchottFHeat fluxes of the Indian Ocean from a global eddy-resolving modelJ. Geophys. Res.1997102C9211472115910.1029/97JC01585 MoninA SOboukhovA MDimensionless turbulence parameters in the atmospheric surface layerDokl. Akad. Nauk SSSR1953932223226 Solov’evA VOn the dissipation of turbulent energy in the layer of wind-driven oceanIzv. AN SSSR: Fiz. Atmos. Okeana1986224380388 ThorpeS AAn Introduction to Ocean Turbulence2007CambridgeCambridge University Press10.1017/CBO9780511801198 Miropol’skiiYu ZNonstationary model of wave-convection mixing layer in the oceanIzv. AN SSSR: Fiz. Atm. Okeana197061212841294 AgoshkovV IIpatovaV MZalesnyV BmuzinE I P-ShutyaevV PProblems of variational assimilation of observational data for ocean general circulation models and methods for their solutionIzv., Atmos. Ocean. Phys.201046667771210.1134/S0001433810060034 (6485_CR26) 1977 G Madec (6485_CR5) 2008 S N Moshonkin (6485_CR35) 2000 W G Large (6485_CR32) 2004 W H Munk (6485_CR3) 1948; 7 S N Moshonkin (6485_CR10) 2007; 47 R C Pacanovsky (6485_CR15) 1981; 11 J D Smith (6485_CR28) 1977; 82 Yu Z Miropol’skii (6485_CR24) 1970; 6 B Galperin (6485_CR7) 1988; 45 V B Zalesny (6485_CR12) 2009; 24 W G Large (6485_CR6) 1994; 32 A S Monin (6485_CR2) 1953; 93 A N Kolmogorov (6485_CR16) 1942; 6 S A Thorpe (6485_CR33) 2007 J C Warner (6485_CR9) 2005; 8 V P Kochergin (6485_CR17) 1977 S N Moshonkin (6485_CR23) 2011; 26 P G Suffman (6485_CR19) 1970; 317 A V Solov’ev (6485_CR27) 1986; 22 M M Zaslavskii (6485_CR25) 2006; 46 G L Mellor (6485_CR4) 1982; 20 V I Agoshkov (6485_CR13) 2010; 46 M Steele (6485_CR30) 2001; 14 A Howard (6485_CR20) 2002; 32 U Garternicht (6485_CR29) 1997; 102 V B Zalesny (6485_CR11) 2010; 25 N A Diansky (6485_CR14) 2002; 38 A S Monin (6485_CR34) 1981 G I Marchuk (6485_CR21) 1980 S M Griffies (6485_CR31) 2000; 2 W Maslovski (6485_CR1) 2008 V M Canuto (6485_CR8) 2001; 31 H Burchard (6485_CR18) 1999 G I Marchuk (6485_CR22) 1988 |
| References_xml | – reference: MadecGNEMO ocean engine (version 3.2). Laboratoire d’Oc’eanographie et du Climat: Expérimentation et Approches Num’eriques. Note du Pôle de modélisation de l’Institut Pierre-Simon Laplace, No. 272008 – reference: KrausE BModelling and Prediction of the Upper Layers of the Ocean1977 – reference: HowardAChengYDubovikovM SOcean turbulence. Part II: Vertical diffusivities of momentum, heat, salt, mass, and passive scalarsJ. Phys. Oceanogr.200232124026410.1175/1520-0485(2002)032<0240:OTPIVD>2.0.CO;2 – reference: MarchukG IMethods of Computational Mathematics1980MoscowNauka – reference: MellorG LYamadaTDevelopment of a turbulence closure model for geophysical fluid problemsRev. Geophys.198220485187510.1029/RG020i004p00851 – reference: MaslovskiWKinneyJ CMarbleDTowards Eddy-Resolving Models of Arctic Ocean. Ocean Modelling in an Eddying Regime. Geophysical Monograph Series 177. 10.1029/177GM162008 – reference: SuffmanP GA model for inhomogeneous turbulent flowProc. R. Soc., Lond. A197031741743310.1098/rspa.1970.0125 – reference: WarnerJ CSherwoodC RArangoH GSignellR PPerformance of four turbulence closure models implemented using a generic length scale methodOcean Modelling200581–28111310.1016/j.ocemod.2003.12.003 – reference: MoninA SOzmidovR VOceanic Turbulence1981LeningradGidrometeoizdat – reference: GalperinBKanthaLHHassidSRosatiAA quasi-equilibrium turbulent energy model for geophysical flowsJ. Atmos. Sci.198845556210.1175/1520-0469(1988)045<0055:AQETEM>2.0.CO;2 – reference: DianskyN ABagnoA VZalesnyV BSigma model of global ocean circulation and its sensitivity to variations in wind stressIzv., Atmos. Ocean. Phys.2002384477494 – reference: ZalesnyV BMarchukG IAgoshkovV IBagnoA VGusevA VDianskyN AMoshonkinS NTamsaluRVolodinE MNumerical modeling of large-scale ocean circulation based on the multicomponent splitting methodRuss. J. Numer. Anal. Math. Modelling201025658160910.1515/rjnamm.2010.036 – reference: AgoshkovV IIpatovaV MZalesnyV BmuzinE I P-ShutyaevV PProblems of variational assimilation of observational data for ocean general circulation models and methods for their solutionIzv., Atmos. Ocean. Phys.201046667771210.1134/S0001433810060034 – reference: KocherginV PKlimokV ISukhorukovV AThe homogeneous layer of the ocean within “differential” modelsNumerical Methods of Continuum Mechanics1977NovosibirskComputing Center of SR RAS102114 – reference: CanutoV MHowardAChengYDubovikovM SOcean turbulence I: One-point closure model. Momentum and heat vertical diffusivitiesJ. Phys. 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| SubjectTerms | Algorithms Climatology Earth and Environmental Science Earth Sciences Geophysics/Geodesy Kinetic energy Marine Ocean circulation Oceanic turbulence Oceanography Simulation Turbulence Upper ocean Water circulation |
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