Notes_AOS200A - Contents 1 Atmos Ocean Thermodynamics 1.1...

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Contents 1 Atmos & Ocean Thermodynamics 5 1.1 Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.1.1 Systems & States . . . . . . . . . . . . . . . . . . . . . . 8 1.1.2 Thermodynamic Processes & Equilibrium . . . . . . . . . 10 1.1.3 Temperature . . . . . . . . . . . . . . . . . . . . . . . . 10 1.1.4 Equations of State . . . . . . . . . . . . . . . . . . . . . 11 1.2 The First Law and its Consequences . . . . . . . . . . . . . . . . 15 1.2.1 The Calculus . . . . . . . . . . . . . . . . . . . . . . . . 17 1.2.2 Some Consequences of the First Law . . . . . . . . . . . 21 1.3 The Second Law and its Consequences . . . . . . . . . . . . . . . 25 1.3.1 Carnot Cycles . . . . . . . . . . . . . . . . . . . . . . . . 25 1.3.2 The Second Law . . . . . . . . . . . . . . . . . . . . . . 26 1.3.3 The Clausius Inequality . . . . . . . . . . . . . . . . . . 27 1.3.4 Entropy . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 1.3.5 Some Consequences of the Second Law . . . . . . . . . . 30 1.4 Phase Changes . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 1.4.1 Clausius Clapeyron . . . . . . . . . . . . . . . . . . . . . 36 1.4.2 Condensate . . . . . . . . . . . . . . . . . . . . . . . . . 38 1.4.3 Moist Enthalpy . . . . . . . . . . . . . . . . . . . . . . . 39 1.4.4 Equivalent Potential Temperature . . . . . . . . . . . . . 40 2 Thermodynamic Processes, and Convection 45 2.1 Aerological Diagrams . . . . . . . . . . . . . . . . . . . . . . . . 45 2.1.1 Pseudo-Adiabats . . . . . . . . . . . . . . . . . . . . . . 49 2.1.2 Polytropic Processes . . . . . . . . . . . . . . . . . . . . 51 2.1.3 Soundings . . . . . . . . . . . . . . . . . . . . . . . . . . 52 2.2 Mixing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 2.2.1 Saturation by isobaric mixing . . . . . . . . . . . . . . . 54 2.2.2 Buoyancy Reversal . . . . . . . . . . . . . . . . . . . . . 55 1
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2 CONTENTS 2.2.3 Mixing Diagrams . . . . . . . . . . . . . . . . . . . . . . 56 2.3 Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 2.3.1 Moist convective instability . . . . . . . . . . . . . . . . 59 2.3.2 CAPE . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 2.3.3 Oceanic convection . . . . . . . . . . . . . . . . . . . . . 63
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Preface These notes emerged from a graduate course which I used to teach at the Uni- versity of California Los Angeles. The course was ten weeks and tried to set the foundations for subsequent studies of convection and small scale processes in the atmosphere. In this version I try to capture some of the main ideas from these notes, augmented by material on ocean thermodynamics. My emphasis is on a the- oretical development of the subject matter. The phenomenology is developed in a parallel class Atmospheric & Oceanic Sciences 200B. Sources for these notes and suggestions for further reading are provided in the section on “Further Reading” at the end of each Chapter. 3
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4 CONTENTS
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Chapter 1 Atmosphere and Ocean Thermodynamics 1.1 Structure The atmosphere, or air, as we experience it, is a multi-component gas in which a great variety (if not great amount) of finescale particulate matter is suspended. The gas phase constituents include several major gases (Nitrogen, Oxygen, Argon) which through the current era have existed in a relatively fixed proportion to one another. To a large degree these determine the thermodynamic properties of what we called dry air, that is an ideal mixture composed of 78.11% N 2 , 20.96% O 2 and 0.93% Ar. Real air contains slightly less of each of these constituents so as to accommodate variable vapors such as carbon dioxide and water, along with a host of seemingly minor gases (e.g., Neon, Helium, Methane, Nitrous Oxide, Ozone) some of which can be important for determining the radiative properties of the at- mosphere and the quality of the air we breath. Of the variable constituents, water is the most striking as it ranges from abundances of nearly zero to as much as 4% by volume. Because of its proclivity to change phase and the manner in which these phase changes affect the local temperature on the one hand, and foster diverse inter- actions with radiant energy on the other, water has the capacity to strongly interact with atmospheric flows over a range of timescales, from minutes to millennia or longer. In this sense the simplest, accurate description of the dynamic atmosphere
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