1. Chapter 1 Governing Equations of the Atmospheric Motion
NCAT/EES Dynamic Meteorology Dr. Yuh-Lang Lin
Chapter 1 Governing Equations of the Atmospheric Motion
1.1 Introduction
Fundamental laws of geophysical fluid dynamics (GFD) and thermodynamics are applied to describe the
(a) atmospheric motions, (u, v, w) [Mechanics]
(b) states of the atmosphere, (r, p, T)
[Thermodynamics]

2. The relationship among different branches of Fluid Dynamics
+stratification
+rotation
GFD
Dynamic Meteorology
Dyn./Phy. Oceanography
Outer Core Dynamics
Dyn. Planet. Atmos.
(+magnetic & electric forces)
e.g., (+dust for Mars)
(+moisture)
(+salinity)

3. Flow motion and states are then expressed by the PDE’s:
By assuming the atmosphere as a continuous fluid medium, a set of partial differential equations (PDE) governing the atmospheric motions are then derived.
Flow motion and states are then expressed by the PDE’s:
flow motion: u, v, w (velocities in x, y, & z directions, resp.)
fluid states: r, T, p (density, temperature, & pressure)
physical variables: humidity, water vapor, cloud water, rain,
ice, snow, hail, air pollutants, chemical species, etc.
Stable ascent over upslope of a large mountain,
Convective precipitating system triggered by the release of instability,
orographic rain over small hills by seeeder-feeder mechanism.

4. Objectives: to understand the mechanisms for atmospheric motions and processes and to help predict the weather.
Approaches
Solve PDEs analytically by making approx.
Dynamic Meteorology
Solve PDEs approximately by computers
Numerical Weather Prediction
Combination of the above approaches
Synoptic-Dynamic Meteorology

5. The relationship among different branches of Atmospheric Sciences and Meteorology
Climatology
Air Pollution/ Atmospheric Chemistry
Physical Meteorology
Dynamic Meteorology
Synoptic Meteorology
Numerical Weather Prediction
Synoptic- Dynamic Meteorology