Abstract
An ocean general circulation model (OGCM) of the Marchuk Institute of Numerical Mathematics of the Russian Academy of Sciences with embedded k–ω vertical turbulent exchange model is developed based on the equations for turbulence kinetic energy k and energy dissipation frequency ω. The solution of the k–ω model equations depends on the frequencies of buoyancy and velocity shift simulated by the OGCM, and the coefficients of vertical turbulence depend on k and ω. The numerical algorithms of both models are based on the method of splitting by the physical processes. The k-ω model equations are split into two stages describing the three-dimensional transport-diffusion of the turbulence kinetic energy k and frequency ω and their local generation-dissipation. The system of ordinary differential equations, arising at the second stage, is solved analytically, which ensures algorithm efficiency. The analytical solution of the equation is also obtained for the vertical turbulence coefficient. The model is used to study the sensitivity of the model circulation of the North Atlantic–Arctic Ocean to variations in the parameters of vertical turbulence. The experiments show that varying the coefficients of the analytical solution of the k–ω model can improve the adequacy of the simulation. The preliminary comparison of the features of the k–ω and k–ε turbulence models is presented using the method of splitting when they are employed in the OGCM.
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REFERENCES
V. B. Zalesny and A. V. Gusev, “Mathematical model of the World Ocean dynamics with algorithms of variational assimilation of temperature and salinity fields,” Russ. J. Numer. Anal. Math. Modell. 24 (2), 171–191 (2009).
V. B. Zalesny, G. I. Marchuk, V. I. Agoshkov, A. V. Bagno, F. V. Gusev, N. A. Diansky, S. N. Moshonkin, E. M. Volodin, and R. Tamsalu, “Numerical modeling of the large-scale ocean circulation on the base of multicomponent splitting method,” Russ. J. Numer. Anal. Math. Modell. 25 (6), 581–609 (2010).
E. M. Volodin, N. A. Diansky, and A. V. Gusev, “Simulating present-day climate with the INMCM4.0 coupled model of the atmospheric and oceanic general circulations,” Izv., Atmos. Ocean. Phys. 46 (4), 414–431 (2010).
V. B. Zalesny, N. A. Diansky, V. V. Fomin, S. N. Moshonkin, and S. G. Demyshev, “Numerical model of the circulation of the Black Sea and the Sea of Azov,” Russ. J. Numer. Anal. Math. Modell. 27 (1), 95–111 (2012).
R. A. Ibrayev, R. N. Khabeev, and K. V. Ushakov, “Eddy-resolving 1/10° model of the World Ocean,” Izv., Atmos. Ocean. Phys. 48 (1), 37–46 (2012).
V. L. Perov, “Calculation of turbulent mixing coefficients on the basis of the spectral algorithm and its use in the COSMO-RU model,” Tr. Gidromettsentra RF, No. 347, 81–94 (2012).
J. C. Warner, C. R. Sherwood, H. G. Arango, and R. P. Signell, “Performance of four turbulence closure models implemented using a generic length scale method,” Ocean Model. 8 (1–2), 81–113 (2005).
W. G. Large, J. C. McWilliams, and S. C. Doney, “Oceanic vertical mixing: A review and a model with a nonlocal boundary layer parameterization,” Rev. Geophys. 32 (4), 363–403 (1994).
V. M. Canuto, A. M. Howard, Y. Cheng, et al., “Ocean turbulence, III: New GISS vertical mixing scheme,” Ocean Modell. 34 (3), 70–91 (2010).
S. N. Moshonkin, V. B. Zalesny, and A. V. Gusev, “A splitting turbulence algorithm for mixing parameterization in the ocean circulation model, IOP Conf. Ser.: Earth Environ. Sci. 231, 012038 (2019). https://doi.org/10.1088/1755-1315/231/1/012038
M. M. Zaslavskii, V. B. Zalesny, I. M. Kabatchenko, and R. Tamsalu, “On the self-adjusted description of the atmospheric boundary layer, wind waves, and sea currents,” Oceanology (Engl. Transl.) 46 (2), 159–169 (2006).
Y. Noh, H. Ok, E. Lee, et al., “Parameterization of Langmuir circulation in the ocean mixed layer model using LES and its application to the OGCM,” J. Phys. Oceanogr. 46 (1), 57–78 (2016).
S. N. Moshonkin, V. B. Zalesny, and A. V. Gusev, “Simulation of the Arctic–North Atlantic Ocean circulation with a two-equation k-omega turbulence parameterization,” J. Mar. Sci. Eng. 95 (6), 1–23 (2018). https://doi.org/10.3390/jmse6030095
S. N. Moshonkin, V. B. Zalesny and A. V. Gusev, “Algorithm of the k–ω turbulence equations solution for the ocean general circulation model,” Izv., Atmos. Ocean. Phys. 54 (5), 495–506 (2018).
G. I. Marchuk and V. B. Zalesny, “Modeling of the World ocean circulation with the four-dimensional assimilation of temperature and salinity fields,” Izv., A-tmos. Ocean. Phys. 48 (1), 15–29 (2012).
V. B. Zalesny, V. I. Agoshkov, V. P. Shutyaev, F. Le Dimet, and B. O. Ivchenko, “Numerical modeling of ocean hydrodynamics with variational assimilation of observational data,” Izv., Atmos. Ocean. Phys. 52 (4), 431–442 (2016).
N. G. Yakovlev, “Coupled model of ocean general circulation and sea ice evolution in the Arctic Ocean,” Izv., Atmos. Ocean. Phys. 39 (3), 355–368 (2003).
H. Burchard, K. Bolding, and M. Villarreal, GOTM, A General Ocean Turbulence Model: Theory, Implementation and Test Cases (Space Applications Institute, 1999). https://books.google.ru/books?id=zsJUHAAACAAJ.
B. Blanke and P. Delecluse, “Variability of the tropical Atlantic Ocean simulated by a general circulation model with two different mixed-layer physics,” J. Phys. Oceanogr. 23 (7), 1363–1388 (1993).
G. Mellor and T. Yamada, “A hierarchy of turbulence closure models for planetary boundary layers,” J. Atmos. Sci. 31 (7), 1791–1806 (1974).
W. G. Large and S. G. Yeager, “The global climatology of an interannually varying air–sea flux,” Clim. Dyn. 33, 341–364 (2009).
C. de Boyer Montégut, G. Madec, A. Fischer, A. Lazar, and D. Iudicone, “Mixed layer depth over the global ocean: An examination of profile data and a profile-based climatology,” J. Geophys. Res.: Oceans 109 (C12) (2004). https://doi.org/10.1029/2004JC002378
R. A. Locarnini, A. V. Mishonov, J. I. Antonov, et al., World Ocean Atlas 2009, Vol. 1: Temperature, Ed. by S. Levitus, NOAA Atlas NESDIS 68 (U.S. Government Printing Office, Washington D.C., 2010).
J. I. Antonov, D. Seidov, T. P. Boyer, R. A. Locarnini, A. V. Mishonov, H. E. Garcia, O. K. Baranova, M. M. Zweng, and D. R. Johnson, World Ocean Atlas 2009, Vol. 1: Salinity, Ed. by S. Levitus, NOAA Atlas NESDIS 69 (U.S. Government Printing Office, Washington D.C., 2010).
Funding
This work was performed at the Marchuk Institute of Numerical Mathematics, Russian Academy of Sciences, with support from the Russian Science Foundation, grant no. 18-11-00163, and from the Russian Foundation for Basic Research, grant no. 18-05-00177.
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Translated by L. Mukhortova
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Zalesny, V.B., Moshonkin, S.N. Sensitivity of the Ocean Circulation Model to the k-ω Vertical Turbulence Parametrization. Izv. Atmos. Ocean. Phys. 55, 470–479 (2019). https://doi.org/10.1134/S0001433819050141
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DOI: https://doi.org/10.1134/S0001433819050141