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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) Rotating reference frame. Coriolis force. Centrifugal force. Tangent plane approximation (V2.1, MP6.6.2, 6.6.3, 6.6.5) Conservation of mass. Continuity equation. Divergenceless flow. Continuity equation in pressure coordinates. (MP6.3)
slides
- Week 2: Thermodynamic equation for an ideal gas (MP6.4) Scaling analyisis. Hydrostatic approximation. Standard approximation. Coriolis parameter. Balanced flow. Geostrophic balance. Rossby number. (MP7.1) Geostrophic flow in pressure coordinates. (MP7.1.1) Synoptic charts. (MP7.1.2) Taylor columns. (MP7.2)
slides (updated 1/15/08)
- Week 3: Thermal wind relation in the assumption of small density variations (MP7.3) Thermal wind relation in pressure coordinates (MP7.3.5) Friction. Molecular and eddy viscosity (V1.3.3, 2.12, 2.12.1) Ekman flow (MP7.4)Ageostrophic flow in atmospheric highs and lows. (MP7.4.2) Planetary scale ageostrophic flow (MP7.4.3) Equations of motion in natural coordinates. Cyclostrophic flow. (MP7.1.3)
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- Week 4: Gradient wind flow. (MP7.1.3) Inertial circles. (MP6.6.4) 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) Large scale atmospheric circulation. Hadley cell. Absolute vorticity conservation. (PM8.1, PM8.2)
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- Week 5: Midlatitude eddies. Baroclinic instability. (MP8.2.2) Energetics of atmospheric large scale circulation. Heat and momentum budget. (PM8.3, PM8.4, PM8.5) Shallow water equations. (V3.1.1 V3.1.2) Shallow water potential vorticity (V3.6.1) Geostrophic adjustment (V3.8.1 V3.8.2 MP7.3.3 MP7.3.4)
slides
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