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Derivation and Assessment of a Mixed Layer Sub-mesoscale Model : Volume 6, Issue 3 (17/09/2009)

By Canuto, V. M.

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Book Id: WPLBN0004021077
Format Type: PDF Article :
File Size: Pages 36
Reproduction Date: 2015

Title: Derivation and Assessment of a Mixed Layer Sub-mesoscale Model : Volume 6, Issue 3 (17/09/2009)  
Author: Canuto, V. M.
Volume: Vol. 6, Issue 3
Language: English
Subject: Science, Ocean, Science
Collections: Periodicals: Journal and Magazine Collection, Copernicus GmbH
Historic
Publication Date:
2009
Publisher: Copernicus Gmbh, Göttingen, Germany
Member Page: Copernicus Publications

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Dubovikov, M. S., & Canuto, V. M. (2009). Derivation and Assessment of a Mixed Layer Sub-mesoscale Model : Volume 6, Issue 3 (17/09/2009). Retrieved from http://www.worldebookfair.org/


Description
Description: NASA, Goddard Institute for Space Studies, New York, NY, 10025, USA. Present studies of mixed layer sub-mesoscales rely primarily on high resolution numerical simulations. Only few of these studies have attempted to parameterize the ensuing buoyancy submesoscale fluxes in terms of the resolved fields so that they can be used in OGCMs (ocean circulation models) that do not resolve sub-mesoscales. In reality, OGCMs used in climate studies include a carbon-cycle which also requires the flux of a passive tracer.

The goal of this work is to derive and assess a parameterization of the submesoscale vertical flux of an arbitrary tracer in terms of the resolved fields. The parameterization is obtained by first solving the dynamic equations governing the velocity and tracer fields that describe sub-mesoscales and then constructing second-order moments such as the tracer fluxes. A key ingredient of the present approach is the modeling of the non-linear terms that enter the dynamic equations of the velocity and tracer fields, a problem that we discuss in two Appendices.

The derivation of the sub-mesoscale tracer vertical flux is analytical and can be followed in detail since no additional information is required. The external forcing includes both baroclinic instabilities and wind stresses.

We compare the model results with data from sub-mesoscale resolving simulations available in the literature which are of two kinds, one with no wind (baroclinic instabilities only) and the other with both baroclinic instabilities and wind. In both cases, the model results reproduce the simulation data satisfactorily.


Summary
Derivation and assessment of a mixed layer sub-mesoscale model

Excerpt
Batchelor, G. K.: The theory of homogeneous turbulence, Cambridge Univ. Press, Cambridge, UK, 195 pp., 1970.; Boccaletti, G., Ferrari, R., and Fox-Kemper, B.: Mixed layer instabilities and restratification, J. Phys. Oceanogr., 37, 2228–2250, 2007.; Canuto, V. M. and Dubovikov, M. S.: A new approach to turbulence, Int. J. Mod. Phys., 12(18), 3121–3152, 1997.; Canuto, V. M. and Dubovikov, M. S.: Modeling mesoscale eddies, Ocean Model., 8, 1–30, 2005, cited as CD5.; Canuto, V. M. and Dubovikov, M.S.: Dynamical model of mesoscales in z-coordinates, Ocean Model., 11, 123–166, 2006, cited as CD6.; Canuto, V. M., Dubovikov, M. S., Luneva, M., Clayson, C. A., and Leboissetier, A.: Modeling mixed layer mesoscales, Ocean Sci. Discuss., in preparation, 2009.; Capet, X., McWilliams, J. C., Molemaker, M. J., and Shchepetkin, A. F.: Mesoscale to submesoscale transition in the California current system. Part 1: flow structure, eddy flux, and observational tests, J. Phys. Oceanogr., 38, 29–43, 2008.; Chasnov, J. R.: Simulation of Kolmogorov inertial subrange using an improved subgrid model, Phys. Fluids, A3, 188–193, 1971.; de Boyer Montegut, C., Madec, G., Fisher, A. S., Lazar, A., and Iudicone, D.: Mixed layer depth over global ocean: an examination of profile data and a profile-based climatology, J. Geophys. Res., 109, C12003, doi: 10.1029/2004JC002378, 2004.; de Boyer Montegut, C., Madec, G., Fisher, A.S., Lazar, A., and Iudicone, D.: Mixed layer depth over global ocean: an examination of profile data and a profile-based climatology, J. Geophys. Res., 109, C12003, doi: 10.1029/2004JC002378, 2004.; Fox-Kemper, B., Ferrari, R., and Hallberg, R.: Parameterization of mixed layer eddies 1: theory and diagnostics, J. Phys. Oceanogr., 38, 1145–1165, 2008.; Fox-Kemper, B. and Ferrari, R.: Parameterization of mixed layer eddies II: prognostics and impact, J. Phys. Oceanogr., 38, 1166–1179, 2008.; Killworth, P. D.: On parameterization of eddy transport, J. Marine Res., 55, 1171–1197, 1997.; Herring, J. R. and Kraichnan, R. H.: Comparison of some approximations for isotropic turbulence, in: Statistical Models and Turbulence, edited by: Rosenblatt, M. and Van Atta, C., Springer-Verlag, New York, 147–194, 1971.; Hosegood, P. J., Gregg, M. C., and Alford, M. H.: Restratification of the Surface Mixed Layer with Submesoscale Lateral Density Gradients: Diagnosing the Importance of the Horizontal Dimension, J. Phys. Oceanogr. 38, 2438–382460, 2008.; Killworth, P. D.: Parameterization of eddy effect on mixed layer tracer transport: a linearized eddy perspective, J. Phys. Oceanogr., 35, 1717–1725, 2005.; Klein, P., Hua, B. L., Lapeyre, G., Capet, X., Le Gentil, S., and Sasaki, H.: Upper ocean turbulence from high resolution 3D simulation, J. Phys. Oceanogr., 38, 1748–1763, 2008.; Kraichnan, R. H.: An almost Markovian Galilean invariant turbulence model, J. Fluid Mech., 47, 513–524, 1971.; Kraichnan, R. H.: Statistical dynamics of two-dimensional flow, J. Fluid Mech., 67, 155–171, 1975.; Lapeyere, G., Klein, P., and Hua, B.C.: Oceanic re-stratification forced surface frontogenesis, J. Phys. Oceanogr., 36, 1577–1590, 2006.; Leith, C. E.: Atmospheric predictability and two-dimensional turbulence, J. Atmos. Sci., {28,} 145–161, 1971.; Lesieur, M.: Turbulence in Fluids, Kluwer, Dordrecht, 212 pp., 1990 (Sect. 3.3).; Levy, M., Klein, P., and Treguier, A. M.: Impacts of sub-mesoscale physics on production and subduction of phytoplankton in an oligotrophic regime, J. Mar. Res., 59, 535–565, 2001.; Levy, M., Klein, P., and Treguier, A. M., Iovino, D., Madec, G., Masson, S., and Takahashi, K.: Modification of gyre circulation by submesoscale physics, Ocean Model., in press, 2009.; Mahadevan, A.: Modeling vertical motion at ocean fronts: Are non-hydrostatic effects relevant to sub-mesoscales?, Ocean Model., 14, 222–240, 2006.; Mahadevan, A. and Tandon, A.: An analysis of mechan

 

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