It is important to characterize the wind shear and turbulence in
the Titan atmosphere with DWE measurements of the smaller-scale
probe motion due to wind gusts (Strobel & Sicardy 1995).
To a good approximation (Atkinson 1989), the probe response to
a horizontal wind gust of magnitude
, applied at time t = 0, is given by:
where 
is the terminal velocity
determined from the force balance (7) between gravity
and the drag force (for 
= 0) given by
Referring to (18), the Probe evidently adjusts itself to the wind on time scales of the order of:
The relaxation time constant 
at some level in the
atmosphere is equal to
the ratio of the probe terminal velocity 
to the acceleration of gravity g at that level.
Both the descent velocity (19) and the probe response
time (20) vary with atmospheric density as
.
If the Probe suddenly encounters a wind gust, the probe horizontal velocity will adjust itself to a factor (1 - 1/e), or about 63% of the gust velocity, in a time equal to the time constant (20). In this time the Probe has descended through a distance
Wind shears contained within a spatial layer smaller than
will have essentially no effect on the Probe.
The spatial scale 
thus represents the minimum (vertical)
size of atmospheric structure detectable by monitoring the PRL Doppler
profile.
Invoking (19) and (20),
it is seen that 
is inversely proportional to the atmospheric
density and independent of g:
Using the Titan atmospheric pressures and densities from
Lellouch et al. (1989),
the probe descent velocity
, response time 
, and minimum scale
sizes 
are tabulated in Table 1, based on the nominal
descent profile of duration 135 min.
Under the initially large parachute (
8 kg/mē) in the upper atmosphere
(above 
115 km), the probe motion will reflect atmospheric
structure with kilometer size scales.
Near the surface, where 
> 50 kg/mē
and 
much smaller, the minimum
detectable structure size is of the order of 20 meters.
Next: 3.3 Doppler Wind Recovery
Up: 3.2 Titan atmospheric descent:
Previous: 3.2.1 Probe motion during
