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Notes
Homework
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References are in general to Marshall and Plumb book, "Atmosphere, Ocean, and Climate Dynamics". E.g., MP1.2 indicates chapter 1, section 2 of Marshall and Plumb book.
Sections of Geoff Vallis' book, "Atmospheric and Oceanic Fluid Dynamics", will be covered. E.g., V1.2 indicates chapter 1, section 2 of Vallis' book. Similarly, H2.1 refers to Holton's book, 'An introduction to dynamic meteorology'.
- Week 0: This class assumes students to have some basic information on atmospheric structure and thermodynamics. Those are the required information: Equation of state (MP1.3.1); Vertical structure of pressure and density (MP3.2, 3.3); Static stability and gravity waves (MP4.2, 4.4); Geopotential height (MP5.2).
- Week 1: Equations of motion. Differentiation following the motion. Lagrangian and Eulerian derivatives (MP6.1). Momentum conservation.
Gravitational force. Pressure gradient force. Frictional force (MP6.2, V1.3.3, V12.2, V2.12.1) Rotating reference frame. Coriolis force. Centrifugal force. Tangent plane approximation (V2.1, MP6.6.2, 6.6.3, 6.6.5)
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- Week 2: Conservation on mass. Continuity equation. Divergenceles Flow. (MP6.3) Equation of state (MP9.1.3). Scaling analysis (V1.11). Hydrostatic approximation. Standard approximation. Coriolis parameter. Balanced flow. Geostrophic balance. Rossby number. (MP7.1) Taylor columns (MP7.2) Geostrophic currents (MP9.3)
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- Week 3: Thermal wind equations (MP7.3). Inertial flow (MP6.6.4) Ekman flow (MP7.4). Ekman pumping (MP10.1). Sverdrup theory (MP10.3).
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- Week 4: Circulation. Kelvin's circulation theorem (H4.1) Relative vorticity. Planetary vorticity. Absolute vorticity. (H4.2) Vorticity equation in a rotating frame (V4.2, V4.4). Western boundary currents. (MP10.2) Abyssal circulation (MP11.3)
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- Week 5: Shallow water equations (V 3.1.1, 3.1.2) Linearized shallow water equations. Poincare' waves. Kelvin waves.
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