Holton, 1.3 –1.4.1
Scale analysis – estimating the magnitudes of various terms
Typical expected values for various quantities are specified:
- Magnitudes of field variables
- Amplitudes of fluctuations
- Characteristic length, depth and time scales of the fluctuations
These values are used to estimate and compare the magnitudes of the various terms in the equations
Eg: a mid-latitude cyclone typically has a 10hPa surface pressure fluctuation and extends across a distance of about 1000 km.
The horizontal pressure gradient is estimated by Pa/m
Pressure fluctuations of 10hPa are common over many systems, such as tornados, squall lines and hurricanes. The differences in spatial scale lead to different terms being dominant in the dynamics of these phenomena.
Fundamental Forces – nature of the forces influencing the atmospheric motions.
Body forces: act on center of mass of fluid parcel. Proportional to parcel mass.
Surface forces: Across boundaries. Independent of mass.
The chief forces in the atmosphere are the pressure gradient, gravity and frictional forces.
In the rotating frame of the earth, the Coriolis force is also important.
Pressure gradient force –
Consider an infinitesimal volume element of air in a box centered on . The molecules in this box are constantly hitting the walls, transferring momentum to it. The force per unit area is given by the pressure. The pressure at the center is , and the pressure at the walls can be approximated as a Taylor expansion to first order in the length of the box.
Then, the sum of the pressure forces acting on opposite walls will be proportional to the negative of the pressure gradient times the volume of the box
*diagrams and equations – enter when I’m at a desk*
The volume times the density is equal to the mass. Dividing both sides by the mass gives the acceleration due to the pressure:
The forces are only proportional to the gradient in the pressure, not its absolute values.