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118 CHAPITRE 4. ETUDES DE PROCESSUS OCÉANOGRAPHIQUES 4.6 Estimation of friction parameters and laws in 1.5D shallow-water gravity currents on the f-plane by data assimilation tel-00545911, version 1 - 13 Dec 2010
4.6. ESTIMATION OF FRICTION PARAMETERS AND LAWS IN 1.5D SHALLOW-WATER GRAVI Ocean Dynamics DOI 10.1007/s10236-008-0151-8 Estimation of friction parameters and laws in 1.5D shallow-water gravity currents on the f-plane, by data assimilation Achim Wirth · Jacques Verron Received: 11 June 2008 / Accepted: 15 September 2008 © Springer-Verlag 2008 tel-00545911, version 1 - 13 Dec 2010 Abstract A 1.5-dimensional, 1.5-layer shallow water model and an ensemble Kalman filter are used to evaluate the feasibility of estimating friction parameters and determining friction laws of oceanic gravity currents. The two friction laws implemented are a linear Rayleigh friction and a quadratic drag law. We demonstrate that the assimilation procedure rapidly estimates the total frictional force, whereas the distinction between the two laws is evolving on a slower time scale. We also demonstrate that parameter estimation can, in this way, choose between different parametrisations and help to discriminate between physical laws of nature by estimating the coefficients presented in such parametrisations. Keywords Ocean dynamics · Gravity current · Friction laws · Parameter estimation · Data assimilation 1 Introduction Buoyancy forces caused by density differences of fluids are a major source of fluid motion in nature. When these forces act adjacent to topography, gravity cur- Responsible Editor: Tal Ezer A. Wirth (B) · J. Verron LEGI / MEOM, CNRS, BP 53, 38041 Grenoble Cedex 9, France e-mail: achim.wirth@hmg.inpg.fr J. Verron e-mail: jacques.verron@hmg.inpg.fr rents are created. The major part of the deep and intermediate waters of the world ocean and marginal seas have done at least part of their voyage to the deep in the form of a gravity current. Oceanic gravity currents play a role of paramount importance in the formation of the water masses of the deep ocean and are thus key to understanding the oceanic component in the earth climate system. For the major part of oceanic gravity currents, the earth’s rotation plays an important role, as they evolve on a timescale much larger than the rotation period of the planet earth. The dominant force balance is, thus, between gravity and the Coriolis force, that is geostrophic. Indeed, when the turbulent fluxes of water masses and momentum are neglected, such gravity currents flow along the inclined ocean floor, changing neither depth nor composition. Turbulent fluxes of tracers, that is mixing, entrainment and/or detrainment, determine the change of the water mass. Together with the turbulent fluxes of momentum at the floor and interface of the gravity current, they determine the change in position of the gravity current. The answer to the question of the evolution of a gravity current lies, thus, in the determination of the laws and parameters of its turbulent fluxes. The inter-comparison study of several ocean general circulation models (OGCMs) (DYNAMO Group 1997; Willebrand et al. 2001) clearly determined the high sensitivity of the meridional heat transport (in the North Atlantic) to the representation of the (Denmark Strait and Faroe Bank Channel) overflows. The meridional heat transport is very sensitive to small-scale details and turbulence in the overflow regions not explicitly resolved in OGCMs and the numerical representation (the grid) of the overflow regions in the OGCMs. Dedicated research on these sub-grid-scale processes is key
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Mémoire de Recherche présenté pa
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Table des matières I Etudes de pro
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Première partie tel-00545911, vers
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Chapitre 1 Avant-propos tel-0054591
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Chapitre 2 Comprendre la dynamique
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2.3. HIÉRARCHIE DE TYPES DE MODÈL
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2.3. HIÉRARCHIE DE TYPES DE MODÈL
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2.5. MA RECHERCHE DANS LE CONTEXTE
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Chapitre 3 Dynamique océanique et
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3.1. LA CIRCULATION OCÉANIQUE À G
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3.1. LA CIRCULATION OCÉANIQUE À G
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3.2. PROCESSUS SUBMÉSO ECHELLES ET
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3.4. RETOUR À LA GRANDE ECHELLE PA
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Bibliographie tel-00545911, version
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Deuxième partie tel-00545911, vers
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33 Curriculum Vitae du Dr. Achim WI
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Colloque bilan LEFE, Plouzané, Mai
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Chapitre 4 Etudes de Processus Océ
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4.1. VARIABILITY OF THE GREAT WHIRL
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4.2. THE PARAMETRIZATION OF BAROCLI
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4.9. ON THE NUMERICAL RESOLUTION OF
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4.9. ON THE NUMERICAL RESOLUTION OF
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Quatrième partie tel-00545911, ver
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175 tel-00545911, version 1 - 13 De
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177 Contents 1 Preface 5 tel-005459
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179 Chapter 1 Preface tel-00545911,
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181 Chapter 2 Observing the Ocean t
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183 Chapter 3 Physical properties o
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185 3.3. θ-S DIAGRAMS 11 3.3 θ-S
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187 3.6. HEAT CAPACITY 13 tel-00545
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189 3.7. CONSERVATIVE PROPERTIES 15
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191 Chapter 4 Surface fluxes, the f
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193 4.2. FRESH WATER FLUX 19 water.
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195 Chapter 5 Dynamics of the Ocean
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197 5.2. THE LINEARIZED ONE DIMENSI
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199 5.4. TWO DIMENSIONAL STATIONARY
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201 5.6. THE CORIOLIS FORCE 27 Whic
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203 5.8. GEOSTROPHIC EQUILIBRIUM 29
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205 5.10. LINEAR POTENTIAL VORTICIT
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207 5.13. A FEW WORDS ABOUT WAVES 3
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209 Chapter 6 Gyre Circulation tel-
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211 6.1. SVERDRUP DYNAMICS IN THE S
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213 6.2. THE EKMAN LAYER 39 In the
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215 6.3. SVERDRUP DYNAMICS IN THE S
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217 Chapter 7 Multi-Layer Ocean dyn
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219 7.3. GEOSTROPHY IN A MULTI-LAYE
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221 7.5. EDDIES, BAROCLINIC INSTABI
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223 Chapter 8 Equatorial Dynamics t
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225 Chapter 9 Abyssal and Overturni
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227 9.2. MULTIPLE EQUILIBRIA OF THE
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229 9.3. WHAT DRIVES THE THERMOHALI
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231 Chapter 10 Penetration of Surfa
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233 10.2. TURBULENT TRANSPORT 59 If
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235 10.5. ENTRAINMENT 61 instabilit
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237 Chapter 11 Solution of Exercise
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239 65 Exercise 32: The moment of i
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241 INDEX 67 Transport stream-funct
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Annexe A Attestation de reussite au
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Annexe B Rapports du jury et des ra
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251 utilisés avec pertinence. Sur
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