I have a problem with most of the answers posted here because I don't
think they reflect the physics of flight.

First, tho', here's the way I picture turbulence.

Turbulence occurs when an aircraft moves from a volume of air moving at
a certain velocity into air moving at a different velocity, and the
transition from one volume of air into the other occurs quickly. It is
important to look at velocity as the combination of speed -and-
direction relative to some reference system. (It is helpful to me to use
a reference system external to the airplane.) So, turbulence may be
caused by updrafts and downdrafts (vertical movement of a body of air
relative to the air surrounding it), or by rapid changes in horizontal
velocity (like the 'swirling air' or 'burbling air' that others have
described).

Another situation in which an airplane may be 'tossed around" is when
one part of the airplane (say the left wing) is in a body of air that is
moving at a different velocity than another part of the aircraft (say
the right wing). Such differentials in velocity aren't likely to exist
for a very long time over such short distances, so they cause a form of
turbulence. So let's say the left wing goes into an updraft, passes
through it quickly, then returns to air that is moving the same velocity
as the right wing; the aircraft will jerk towards the right.

Now to other explanations of the airspeed question: One principle I
believe applies is the First Law of Physics" - "Conservation of Energy"
(see http://en.wikipedia.org/wiki/Conservation_of_energy"). In level
flight, and at a constant power setting, an aircraft whose airspeed is
disturbed -will return- to the airspeed at which it was flying before
the disturbance. The return to that airspeed will be delayed by the
time required to accelerate (or decelerate) until the thrust (power)
matches drag. The amount of time required will be related to the mass
of the airplane and the difference between power produced by the engine
(thrust) and the drag of the aircraft.

In the short span of time during which the aircraft moves from air
moving at the first velocity to the second, the velocity of the air
relative to the aircraft (angle of attack and/or yaw) will change
abruptly, the occupants will feel 'turbulence', and the aircraft will
find itself in a different flight condition. But assuming there isn't
another change in the airmass velocity surrounding the aircraft (or a
change in power setting or trim), it will return to the same flight
attitude as before the change. When there are repeated, frequent
changes in airmass velocity, it will be difficult to observe the effect,
but it -is- a Law of Physics.

As for the proposed explanations that address the pitot/static system:
Once the aircraft has returned to the original airspeed, and assuming
there were no changes in power, trim, or significant change in gross
weight, the plane will be going through the air at the same angle as
before the 'perturbation' - it will be flying at the same angles of
attack and of yaw. So the air pressure sources will be seeing the same
air as before which should result in the same readings on the instruments.

But back to Jay's question: What might explain why airspeed increased
in turbulence? Here's another idea - a phenomenon described in the
April/May 2005 issue of Air & Space Smithsonian, an article that
discusses flying sailplanes and an phenomenon they call "dynamic
soaring". I really don't understand it well, but it seems to be that
one can 'gain energy' for the 'aircraft system' by "exposing the
airplane's belly to stronger winds" for brief periods of time, flying
back into winds not so strong, returning to the stronger winds, and
going back and forth. So, I guess the airplane extracts some energy
from the stronger winds (weakening them I assume), and uses that energy
to go faster (or in the case of sailplanes, stay aloft longer). What do
you think?

George Young
T-34, Comanche, C-182/172/152, Mooney, and Arrow pilot