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Chapter 2. Basic Conservation Laws

z. U (x,y,z,t). mass element. z 0. y 0. y. x 0. x. Chapter 2. Basic Conservation Laws. 2.1 Total Differentiation ( in the Lagrangian frame). Local Temperature Change and Temperature Advection. Example for Advection. p. p(x). 300 Pa. u=10km/h. x. East. West. 180 km.

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Chapter 2. Basic Conservation Laws

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  1. z U(x,y,z,t) mass element z0 y0 y x0 x Chapter 2. Basic Conservation Laws Reinisch_ASD_85.515

  2. 2.1 Total Differentiation(in the Lagrangian frame) Reinisch_ASD_85.515

  3. Local Temperature Change and Temperature Advection Reinisch_ASD_85.515

  4. Example for Advection p p(x) 300 Pa u=10km/h x East West 180 km Reinisch_ASD_85.515

  5. Total Differentiation of a Vector in a Rotating System Reinisch_ASD_85.515

  6. W k i’ i’ j l i Rotation Reinisch_ASD_85.515

  7. Rotating Coordinate System Reinisch_ASD_85.515

  8. 2.2 Momentum Equation in a Rotating Coordinate System Reinisch_ASD_85.515

  9. Absolute Derivation of Ua Reinisch_ASD_85.515

  10. Acceleration in Rotating Frame Reinisch_ASD_85.515

  11. W j U R k i r f 2.3 Using Spherical Coordinates Reinisch_ASD_85.515

  12. 2.3 cont’d Reinisch_ASD_85.515

  13. 2.3 cont’d Reinisch_ASD_85.515

  14. Components of DU/Dt Reinisch_ASD_85.515

  15. 2.4 Scale Analysis (horizontal components) Reinisch_ASD_85.515

  16. 2.41 Geostrophic Approximation Reinisch_ASD_85.515

  17. 2.24 Rossby Number Reinisch_ASD_85.515

  18. 2.4.3 Hydrostatic Approximation Reinisch_ASD_85.515

  19. z dz y z0 dy dx y0 x x0 2.5.1 The Continuity EquationEulerian Derivation Reinisch_ASD_85.515

  20. Eulerian Derivation Reinisch_ASD_85.515

  21. Eulerian Derivation Reinisch_ASD_85.515

  22. Lagrangian Derivation Reinisch_ASD_85.515

  23. UA UB x xB xA Lagrangian Derivation Reinisch_ASD_85.515

  24. Lagrangian Derivation Reinisch_ASD_85.515

  25. 2.5.3 Scale Analysis of the Continuity Equation Reinisch_ASD_85.515

  26. Scale Analysis Reinisch_ASD_85.515

  27. 2.6 Energy Conservation Reinisch_ASD_85.515

  28. Rate of Change of Energy Reinisch_ASD_85.515

  29. Rate of Work Done Reinisch_ASD_85.515

  30. Reinisch_ASD_85.515

  31. Thermal Energy Equation Reinisch_ASD_85.515

  32. Thermodynamic Energy Equation Reinisch_ASD_85.515

  33. Thermodynamics of the Dry Atmosphere Reinisch_ASD_85.515

  34. Potential Temperature Reinisch_ASD_85.515

  35. Adiabatic Lapse Rate Reinisch_ASD_85.515

  36. 2.7.3 Static Stability Reinisch_ASD_85.515

  37. Buoyancy Oscillations Reinisch_ASD_85.515

  38. Buoyancy … Reinisch_ASD_85.515

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