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Numerical Investigation of Algebraic Oceanic Turbulent Mixing-layer Models : Volume 20, Issue 6 (06/11/2013)

By Chacón-rebollo, T.

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Book Id: WPLBN0003990937
Format Type: PDF Article :
File Size: Pages 10
Reproduction Date: 2015

Title: Numerical Investigation of Algebraic Oceanic Turbulent Mixing-layer Models : Volume 20, Issue 6 (06/11/2013)  
Author: Chacón-rebollo, T.
Volume: Vol. 20, Issue 6
Language: English
Subject: Science, Nonlinear, Processes
Collections: Periodicals: Journal and Magazine Collection (Contemporary), Copernicus GmbH
Publication Date:
Publisher: Copernicus Gmbh, Göttingen, Germany
Member Page: Copernicus Publications


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Gómez-Mármol, M., Rubino, S., & Chacón-Rebollo, T. (2013). Numerical Investigation of Algebraic Oceanic Turbulent Mixing-layer Models : Volume 20, Issue 6 (06/11/2013). Retrieved from

Description: Dpto. EDAN & IMUS, Universidad de Sevilla, C/Tarfia, s/n. 41012, Seville, Spain. In this paper we investigate the finite-time and asymptotic behaviour of algebraic turbulent mixing-layer models by numerical simulation. We compare the performances given by three different settings of the eddy viscosity. We consider Richardson number-based vertical eddy viscosity models. Two of these are classical algebraic turbulence models usually used in numerical simulations of global oceanic circulation, i.e. the Pacanowski–Philander and the Gent models, while the other one is a more recent model (Bennis et al., 2010) proposed to prevent numerical instabilities generated by physically unstable configurations. The numerical schemes are based on the standard finite element method. We perform some numerical tests for relatively large deviations of realistic initial conditions provided by the Tropical Atmosphere Ocean (TAO) array. These initial conditions correspond to states close to mixing-layer profiles, measured on the Equatorial Pacific region called the West-Pacific Warm Pool. We conclude that mixing-layer profiles could be considered as kinds of absorbing configurations in finite time that asymptotically evolve to steady states under the application of negative surface energy fluxes.

Numerical investigation of algebraic oceanic turbulent mixing-layer models

Bennis, A. C., Chacón-Rebollo, T., Gómez-Mármol, M., and Lewandowski, R.: Stability of some turbulent vertical models for the ocean mixing boundary layer, Appl. Math. Lett., 21, 128-133, doi:10.1016/j.aml.2007.02.016, 2008.; Bennis, A. C., Chacón-Rebollo, T., Gómez-Mármol, M., and Lewandowski, R.: Numerical modelling of algebraic closure models of oceanic turbulent mixing layers, ESAIM-Math. Model. Num., 44, 1255-1277, doi:10.1051/m2an/2010025, 2010.; Boyer Montégut, C., Madec, G., Fischer, A. S., Lazar, A., and Iudicone, D.: Mixed layer depth over the global ocean: An examination of profile data and a profile-based climatology, J. Geophys. Res., 109, C12003, doi:10.1029/2004JC002378, 2004.; Burchard, H., Bolding, K., Villarreal, M. R., Rippeth, T. P., Fisher, N., and Stips, A.: The GOTM modelling system, in: Marine Turbulence: Theories, Observations and Models, edited by: Baumert, H. Z., Simpson, J. H., and Sündermann, J., Cambridge University Press, 213–224, 2005.; Chacón-Rebollo, T., Gómez-Mármol, M., and Rubino, S.: On the existence and asymptotic stability of solutions for unsteady mixing-layer models, Discrete Cont. Dyn. S.-A, 34, 423–438, doi:10.3934/dcds.2014.34.421, 2013a.; Chacón-Rebollo, T., Gómez-Mármol, M., and Rubino, S.: Analysis of numerical stability of algebraic oceanic turbulent mixing layer models, Appl. Math. Model., under review, 2013b.; Defant, A.: Schichtung und zirkulation des atlantischen ozeans, Wiss. Ergebn.: Deutsch. Atlant. Exp. Forsch., 6, 289–411, 1936.; Gaspar, P., Gregoris, Y., and Lefevre, J.-M.: A simple eddy kinetic energy model for simulation of the oceanic vertical mixing: Tests at Station Papa and long-term upper ocean study site, J. Geophys. Res., 16, 179–193, doi:10.1029/JC095iC09p16179, 1990.; Gent, P. R.: The heat budget of the TOGA-COARE domain in an ocean model, J. Geophys. Res., 96, 3323–3330, doi:10.1029/90JC01677, 1991.; Goosse, H., Deleersnijder, E., Fichefet, T., and England, M. H.: Sensitivity of a global coupled ocean-sea ice model to the parameterization of vertical mixing, J. Geophys. Res., 104, 13681–13695, doi:10.1029/1999JC900099, 1999.; Kowalik, Z. and Murty, T. S.: Numerical modeling of ocean dynamics, World Scientific, Singapore, doi:10.1142/1970, 1993.; Large, W. G., McWilliams, J. C., and Doney, S. C.: Oceanic vertical mixing: A review and a model with a nonlocal boundary layer parameterization, Rev. Geophys., 32, 363–403, doi:10.1029/94RG01872, 1994.; Lemke, P.: A coupled one-dimensional sea ice-ocean model, J. Geophys. Res., 92, 13164–13172, doi:10.1029/JC092iC12p13164, 1987.; Lewandowski, R.: Analyse mathématique et océanographie, Masson, Paris, 1997.; McPhaden, M.: The tropical atmosphere ocean (tao) array is completed, B. Am. Meteorol. Soc., 76, 739–741, 1995.; Mellor, G. and Yamada, T.: Development of a turbulence closure model for geophysical fluid problems, Rev. Geophys., 20, 851–875, doi:10.1029/RG020i004p00851, 1982.; Osborn, T. R. and Cox, C. S.: Oceanic fine structure, Geophys. Fluid Dyn., 3, 321–345, doi:10.1080/03091927208236085, 1972.; Pedlosky, J.: Geophysical fluid dynamics, 2nd Edn., Springer-Verlag, New York and Berlin, 1987.; Pacanowski, R. C. and Philander, S. G. H.: Parameterization of vertic


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