PART IV — DYNAMICS OF THE ATMOSPHERE-OCEAN SYSTEM 



Figure IV-10 — WAVES AND TURBULENCE IN THE CLEAR ATMOSPHERE 



Height (m) 



400 



- 300 



- 200 



1920 



1930 



TIME (PDT) AUGUST 6, 1969 



(Illustration Courtesy of the American Geophysical Union ) 



Radar echoes from the clear atmosphere reveal a group of 

 amplifying and breaking waves in the low-level temperature 

 inversion at San Diego, California, as observed with a special 

 FM-CW radar. Waves are triggered by the sharp change of 

 wind speed across the interface between the cool, moist 

 marine layer and the warmer, drier air aloft. They move 

 through the radar beam at the speed of the wind at their 

 mean height, about 4 knots, so that crests appear at succes- 

 sive stages of development. In the second wave at 1919 PDT 

 cooler air from the wave peak drops rapidly as the breaking 



begins. By 1929 PDT the layer has become fully turbulent, 

 and the radar echo subsequently weakens. Note, too, the 

 secondary waves near the crests at 1919.5, 1922, and 1926 

 PDT; these secondary waves give rise to microscale turbu- 

 lence, which causes the echo layers to be detected. The 

 resulting turbulence would be weak, as detected by an air- 

 craft. Waves of this type occur regularly in the low-level 

 inversion, and are believed to be similar to those which cause 

 the severe turbulence occasionally encountered by jet aircraft 

 at high altitude. 



mediately prior to breaking. The 

 r.m.s. velocity of a vortex, 



Vrms = 0.707 Aoj 



= 0.707 A(tV/(z) (2) 



where A is the amplitude of the roll 

 or wave, to its angular rotation rate 

 or vorticity, and cV/cz the wind 

 shear, thus provides a simple estimate 

 of the expected turbulence; prelimi- 

 nary tests support this hypothesis. 

 Moreover, it is of particular interest 

 that the high-resolution radar data 

 provide direct measures of A and its 

 rate of growth as well as of 5V/?z, 

 the shear. Similarly, the turbulence 

 intensity may be deducted from the 

 r.m.s. perturbations in the echo-layer 

 height subsequent to breaking. (As 

 yet, the inherent doppler capability of 

 the FM-CW radar, which would pro- 

 vide direct measurements of both 

 vertical motion and roll vorticity, has 

 not been implemented.) 



Unresolved Problems — If Equa- 

 tion (2) is validated by experiments 

 now in progress, we may contemplate 

 the prediction of WIT from measure- 

 ments and predictions of maximum 

 wave amplitude and shear. But this 

 assumes that we shall be able to pre- 

 dict the latter. At this writing, the 

 relationship of the maximum wave 

 amplitude to the thermal and wind 

 structure of the environment is not 

 understood. Present K-H wave the- 

 ory is limited to small-amplitude 

 waves and their initial growth rates; 

 clearly, the theory needs to be ex- 

 tended to finite-amplitude waves. But 

 rapid progress is more likely to come 

 from experiments in the real atmos- 

 phere, such as those already men- 

 tioned, which involve somewhat more 

 complex wind and temperature pro- 

 files and interactions than are likely 

 to be tractable in finite-amplitude 

 theoretical models. 



In this regard, it should also be 

 noted that the critical Richardson 

 number, Ri,- < V-i, which might be 

 regarded as a predictor of WIT, refers 

 only to the initial growth stage of 

 K-H instability. Since the high-reso- 

 lution radar shows breaking K-H 

 waves with amplitudes as small as 5 

 meters (with negligible resulting tur- 

 bulence) and as large as 100 meters 

 (with appreciable turbulence), a seri- 

 ous question is raised as to the verti- 

 cal scales over which thermal stabil- 

 ity and shear — and so Ri — need to be 

 measured. Surely, the present data 

 imply that Ri must be observed on 

 scales of a meter or less to account 

 for the small-amplitude waves. But 

 it is not so clear that measurements 

 with resolution of 10 to 100 meters 

 or more, such as those available from 

 present-day radiosondes, would be 

 adequate to predict the occurrence of 

 larger-amplitude waves. What, for 



110 



