Reinisch_ASD_85.5151 Chapter 2. Basic Conservation Laws x0x0 y0y0 z0z0 z y x U(x,y,z,t) mass element.

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Presentation transcript:

Reinisch_ASD_ Chapter 2. Basic Conservation Laws x0x0 y0y0 z0z0 z y x U(x,y,z,t) mass element

Reinisch_ASD_ Total Differentiation ( in the Lagrangian frame)

Reinisch_ASD_ Local Temperature Change and Temperature Advection

Reinisch_ASD_ Example for Advection p East x West p(x) 180 km 300 Pa u=10km/h

Reinisch_ASD_ Total Differentiation of a Vector in a Rotating System

Reinisch_ASD_ Rotation i i’ i’ k  j

Reinisch_ASD_ Rotating Coordinate System

Reinisch_ASD_ Momentum Equation in a Rotating Coordinate System

Reinisch_ASD_ Absolute Derivation of U a

Reinisch_ASD_ Acceleration in Rotating Frame

Reinisch_ASD_ Using Spherical Coordinates  i k j R r  U

Reinisch_ASD_ cont’d

Reinisch_ASD_ cont’d

Reinisch_ASD_ Components of DU/Dt

Reinisch_ASD_ Scale Analysis (horizontal components)

Reinisch_ASD_ Geostrophic Approximation

Reinisch_ASD_ Rossby Number

Reinisch_ASD_ Hydrostatic Approximation

Reinisch_ASD_ The Continuity Equation Eulerian Derivation x y z xx yy zz x0x0 y0y0 z0z0

Reinisch_ASD_ Eulerian Derivation

Reinisch_ASD_ Eulerian Derivation

Reinisch_ASD_ Lagrangian Derivation

Reinisch_ASD_ Lagrangian Derivation xAxA xBxB UAUA UBUB x

Reinisch_ASD_ Lagrangian Derivation

Reinisch_ASD_ Scale Analysis of the Continuity Equation

Reinisch_ASD_ Scale Analysis

Reinisch_ASD_ Energy Conservation

Reinisch_ASD_ Rate of Change of Energy

Reinisch_ASD_ Rate of Work Done

Reinisch_ASD_

Reinisch_ASD_ Thermal Energy Equation

Reinisch_ASD_ Thermodynamic Energy Equation

Reinisch_ASD_ Thermodynamics of the Dry Atmosphere

Reinisch_ASD_ Potential Temperature

Reinisch_ASD_ Adiabatic Lapse Rate

Reinisch_ASD_ Static Stability

Reinisch_ASD_ Buoyancy Oscillations

Reinisch_ASD_ Buoyancy …