Environmental Risks and Disasters
Lecture Notes 5 (02/05/2008)
Atmospheric stability / Mitigation of tornado hazards
The second force, other than gravity, that acts on the air is due to variations in
pressure. To see how this force comes about, consider what happens if we have a
low and a high pressure, like the ones that we see on a weather map. Between the
low and the high pressure on this map, the pressure increases from low to high.
Now, consider a parcel of air sitting somewhere between the low and high. On
one side it will be affected by a lower pressure than on the other, that is it will be
`pushed' harder on one side than on the other. We can use some simple physics to
describe this quantitatively, in particular if we use a diagram.
Consider the air in a tube of cross-sectional area A. The force on the air from the
`low' side is FL = PL x A, on the `high' side FH = PH x A. We can write down
what the net force is by subtracting the two,
F = (PL - PH) x (A)
If we wanted to write this in terms of a force per unit volume, we need to divide
by the volume of the gas, which is V = A x length, and we get
F/V = (PL - PH) / (length)
We see from this equation, that the force acting on a parcel of air with given
volume, is proportional to the gradient (slope) in the pressure. This is, as you
probably realized some time ago, a force that can generate winds, since it pushes
air from high pressures to low pressures.
At sea level, the air pressure does not vary by very much horizontally, normally
perhaps by 10 mb, or 1%. Instead, we all have experienced that pressure varies
quite rapidly in the vertical direction. The human body is quite sensitive to
pressure variations, in particular our ears. If we go to Denver the air pressure is
noticeably different. Denver is at an elevation of 1600 m (approx.), and the air
pressure is around 840 mb. On Mount Everest the pressure is around 400 mb.
Given these large vertical pressure variations, a natural question is why air does
not simply rise, since we just figured out that there should be a force in the
direction towards lower pressures. The answer is that most of the time the upward
force, caused by the pressure gradient, is directly matched by the force of gravity
which pulls the air down. In order to see when this statement breaks down, we