Etudes et évaluation de processus océaniques par des hiérarchies ...
Etudes et évaluation de processus océaniques par des hiérarchies ... Etudes et évaluation de processus océaniques par des hiérarchies ...
178 4 CONTENTS 5.12 The Beta-plane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 5.13 A few Words About Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 6 Gyre Circulation 35 6.1 Sverdrup Dynamics in the SW Model (the math) . . . . . . . . . . . . . . . . . 35 6.2 The Ekman Layer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 6.2.1 Ekman Transport (one layer) . . . . . . . . . . . . . . . . . . . . . . . . 38 6.2.2 The Ekman Spiral . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 6.3 Sverdrup Dynamics in the SW Model (the physics) . . . . . . . . . . . . . . . . 41 tel-00545911, version 1 - 13 Dec 2010 7 Multi-Layer Ocean dynamics 43 7.1 The Multilayer Shallow Water Model . . . . . . . . . . . . . . . . . . . . . . . . 43 7.2 Conservation of Potential Vorticity . . . . . . . . . . . . . . . . . . . . . . . . . 44 7.3 Geostrophy in a Multi-Layer Model . . . . . . . . . . . . . . . . . . . . . . . . . 44 7.4 Barotropic versus Baroclinic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 7.5 Eddies, Baroclinic instability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 7.6 Continuous Stratification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 8 Equatorial Dynamics 49 9 Abyssal and Overturning Circulation 51 9.1 The Stommel Arons Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 9.2 Multiple Equilibria of the Thermohaline Circulation . . . . . . . . . . . . . . . . 53 9.3 What Drives the Thermohaline Circulation? . . . . . . . . . . . . . . . . . . . . 55 10 Penetration of Surface Fluxes 57 10.1 Molecular Transport . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 10.2 Turbulent Transport . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 10.3 Convection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 10.4 Richardson Number . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 10.5 Entrainment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 10.6 Gravity Currents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 11 Solution of Exercises 63
179 Chapter 1 Preface tel-00545911, version 1 - 13 Dec 2010 This course deals with the aspects of physical oceanography which are important to understand the dynamics and role of the ocean in the climate system of our planet earth. There are outstanding and very comprehensive books on the dynamics of the worlds ocean, and the purpose of this Guided Tour Through Physical Oceanography is not to rival them, but rather to provide for a concise, self contained and systematic introduction to the field, emphasizing the basic questions. While teaching an introductory class of physical oceanography to graduate students, I found no concise introduction to the subject that deals with the matter on an advanced and modern level. By modern I mean oriented “[...] toward the understanding of physical processes which control the hydrodynamics of oceanic circulation.” (H. Stommel, The Gulfstream, 1958). More precisely, when considering such physical process we first assume that such process can be modeled by the Navier-Stokes equations, an assumption that is surely satisfied to a very high degree of accuracy. We then proceed in four steps: (i) formulate assumptions about the process that simplify the problem; (ii) use these assumptions to derive simplified (mathematical) models; (iii) study the thus obtained simplified models; and (iv) compare the results to observations (if available) to validate or reject the results. If the results have to be rejected when confronted with observations, laboratory experiments or results from more complete models, we have to formulate new assumptions, that is, restart with (i). It is the first point, the choice of the important assumptions which is key to scientific progress and asks for a deep scientific insight. Today’s research on ocean dynamics is guided by the power of increasingly complex numerical models. These models are, however, so involved, that simpler models are needed to comprehend them and the study of a phenomenon of ocean dynamics passes by the study of a hierarchy of models of increasing complexity. The prerequisites for this guided tour is a course in calculus and some knowledge of elementary fluid dynamics. I try to present the subject “as simple as possible but not simpler” (A. Einstein). It is indeed my conviction that some introductory courses of ocean dynamics are over simplified and are thus impossible to really understand or are plainly wrong. Many important aspects of the ocean circulation are omitted, which is permitted in a guided tour but not so much in a text book. The most important are waves (surface, Poincaré, Kelvin and Rossby), which are not visited by this guided tour. The justification that we are here mostly concerned with the behavior of the ocean on long time scales, relevant to climate dynamics, much longer than the typical time scale of the above mentioned waves, is weak. Including oceanic waves in a self contained and systematic way would easily double the length of this course. I choose not to present figures of observations and data in this course as they are subject to rapid improvement and as their latest version can easily be retrieved from the Internet. The 5
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178<br />
4 CONTENTS<br />
5.12 The B<strong>et</strong>a-plane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32<br />
5.13 A few Words About Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33<br />
6 Gyre Circulation 35<br />
6.1 Sverdrup Dynamics in the SW Mo<strong>de</strong>l (the math) . . . . . . . . . . . . . . . . . 35<br />
6.2 The Ekman Layer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38<br />
6.2.1 Ekman Transport (one layer) . . . . . . . . . . . . . . . . . . . . . . . . 38<br />
6.2.2 The Ekman Spiral . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39<br />
6.3 Sverdrup Dynamics in the SW Mo<strong>de</strong>l (the physics) . . . . . . . . . . . . . . . . 41<br />
tel-00545911, version 1 - 13 Dec 2010<br />
7 Multi-Layer Ocean dynamics 43<br />
7.1 The Multilayer Shallow Water Mo<strong>de</strong>l . . . . . . . . . . . . . . . . . . . . . . . . 43<br />
7.2 Conservation of Potential Vorticity . . . . . . . . . . . . . . . . . . . . . . . . . 44<br />
7.3 Geostrophy in a Multi-Layer Mo<strong>de</strong>l . . . . . . . . . . . . . . . . . . . . . . . . . 44<br />
7.4 Barotropic versus Baroclinic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46<br />
7.5 Eddies, Baroclinic instability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46<br />
7.6 Continuous Stratification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48<br />
8 Equatorial Dynamics 49<br />
9 Abyssal and Overturning Circulation 51<br />
9.1 The Stommel Arons Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52<br />
9.2 Multiple Equilibria of the Thermohaline Circulation . . . . . . . . . . . . . . . . 53<br />
9.3 What Drives the Thermohaline Circulation? . . . . . . . . . . . . . . . . . . . . 55<br />
10 Pen<strong>et</strong>ration of Surface Fluxes 57<br />
10.1 Molecular Transport . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57<br />
10.2 Turbulent Transport . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58<br />
10.3 Convection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60<br />
10.4 Richardson Number . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60<br />
10.5 Entrainment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61<br />
10.6 Gravity Currents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62<br />
11 Solution of Exercises 63
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