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