Oceanography

Oceanography - Geosci 233: Physical Oceanography Douglas R....

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Geosci 233: Physical Oceanography Douglas R. MacAyeal Department of Geophysical Sciences University of Chicago Chicago, Illinois March 28, 2001
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Figure 1: The Atrevida discovering the Aurora Islands. c ° 1994 Douglas R. MacAyeal. All rights reserved. 1
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Contents 1 Maps 8 1.1 Three Classes of Maps . ..................... 8 1.2 Spherical Coordinates . ...................... 1 0 1.3 Map Projections . ........................ 1 2 1.4 Polar Stereographic Projection . ................ 1 2 1.4.1 Lambert Equal-Area Projection . ............ 1 3 1.4.2 Mercator’s Projection . . ................. 1 5 1.4.3 Hammer-AitoF and Mollweide Projections . . ..... 1 9 2 Shape of the Ocean Basins 25 2.1 Sea-±loor Spreading and Continental Drift . . ......... 2 6 2.1.1 Kelvin’s Solution for the Cooling of the Earth . .... 2 9 2.1.2 Laplace Transform . ................... 3 0 2.1.3 Solution of the Subsidiary Equation . 3 1 2
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2.1.4 Inverse Laplace Transform. ............... 3 1 2.1.5 Integrating the Bromwich Integral. ........... 3 3 2.1.6 Geothermal Gradient . . ................. 3 7 2.1.7 Kelvin’s Edinburgh Calculation . ............ 3 8 2.2 Theory of Sea-Floor Subsidence . ................ 3 8 2.3 A Plate Model of Oceanic Crust . 4 2 2.4 Numerical Methods . . ...................... 4 7 2.4.1 Finite-Di±erence Solution as a Matrix Algebra Problem 50 2.5 Hypsometry . . .......................... 5 1 2.6 Assignment: Analysis of Ocean Bathymetry . ......... 5 4 2.6.1 Assignment: Hypsometry of the Earth . ........ 5 5 2.6.2 Assignment: Finite-di±erence model of cooling plate . . 56 3 Hydrography I 59 3.1 Temperature . 6 0 3.2 Sea Surface Temperature. .................... 6 2 3.2.1 Freezing Point of Seawater. 6 2 3.3 Salinity . ............................. 6 3 3.4 Density . 6 5 3.5 Assignment . 6 6 3
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4 Hydrography II 69 4.1 Stratifcation . .......................... 6 9 4.1.1 Available Potential Energy. ............... 7 0 4.1.2 Buoyancy . ........................ 7 1 4.2 A Bouncing Beachball . ..................... 7 3 4.2.1 Internal Gravity Waves . ................. 7 7 4.3 Temperature and Salinity Diagrams . . ............. ± 2 4.3.1 Mixing . ± 2 4.4 Bulk Ocean Properties . ± 3 4.5 Exercises . ............................. ± 4 5 Bogus Forces 90 5.1 The Rotating Plane . . ...................... 9 2 5.1.1 Assignment - Inertial oscillations . ........... 9 4 5.2 Foucault Pendulum . 9 5 5.2.1 Assignment - Foucault pendulum . 9 6 5.3 Description o² Motion at the Earth’s Sur²ace . ......... 9 7 5.3.1 Assignment – Rotating earth coordinates. . . ..... 9 8 6 Geostrophy 103 6.1 Equations Governing Horizontal Motion . 1 0 3 4
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6.2 The Geostrophic Balance. .................... 1 0 5 6.2.1 “Thermal-wind” relationship . . ............. 1 0 5 6.3 Dynamic Topography . ...................... 1 0 6 6.4 Assignment . . .......................... 1 0 7 7 Ekman Pump 110 7.1 Ekman Layer: Conceptual View . ................ 1 1 0 7.2 Ekman Pumping . ........................ 1 1 1 7.3 Ekman Pumping in Geographic Coordinates . ......... 1 1 3 7.4 Upwelling . ............................ 1 1 4 7.5 The Ekman Spiral . . ...................... 1 1 4 7.6 Ekman Transport. 1 1 7 7.7 Assignment . 1 1 8 8 Wind-Driven Ocean Circulation 122 8.1 Two Possible Balances . ..................... 1 2 2 8.2 Basal Ekman Layer Only. 1 2 3 8.2.1 Exercise: An Wind-Driven Circulation Predicted by Incomplete Physics. ................... 1 2 5 8.3 Basal Ekman Layer Plus Divergence of Geostrophic Flow (Sver- drup Balance) . .......................... 1 2 5 8.4 Exercise: A Predicted Wind-Driven Circulation That Satis±es Our Preconceptions . 1 3 1 5
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9 Shallow Water Gravity Waves 133 9.1 Overview . ............................. 1 3 3 9.2 Hydrostatic Balance . ...................... 1 3 4 9.3 Shallow Water Equations. .................... 1 3 5 9.4 Shallow-Water Gravity Waves . ................. 1 3 6 9.5 Particle Motions . ........................ 1 3 7 9.6 Geostrophic Adjustment . 1 4 2 9.6.1 An analytic example .
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Oceanography - Geosci 233: Physical Oceanography Douglas R....

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