ANALYSIS OF DUCTS IN THE TRADE WIND REGIONS 



93 



tabulated above values for the isothermal case. For 

 an intermediate lapse rate some intermediate value 

 holds. 



Table 13. Critical wavelengths in meters for T = 280°A. 



Upper value: incompressible, homogeneous fluids. Lower value: com- 

 pressible, isothermal fluids. 



Thus, for any given inversion, stable wave motion 

 may exist so long as the wavelength is equal to or 

 greater than the listed values and less than about 

 500 km. There is no theoretical reason to believe that 

 any particular wavelength in this wide range is more 

 apt to occur in nature than any other. 



There is, however, some observational evidence to 

 indicate that the wavelengths which occur in the at- 

 mosphere are near the lowest possible values which 

 can occur, namely, the critical values tabulated above. 

 Billow clouds have been observed to occur near in- 

 versions, and there are some ten cases on record where 

 wavelengths of the billows as well as values for the 

 temperature and wind velocity differences have been 

 observed. In these cases the maximum difference be- 

 tween observed wavelength and critical wavelength was 

 48 per cent. In only three cases was the difference 

 greater than 15 per cent.^^'' 



Other weather phenomena have been observed which 

 indicate stable wave motion in the atmosphere. In 

 1936, quite regular fluctuations were measured in 

 ceiling height at San Diego on two occasions. The 

 amplitude of the fluctuations averaged 25 to 30 ra in 

 the two cases, with periods of about 15 to 20 min over 

 time intervals of 4 or 5 hours.-" In 1934 at the Blue 

 Hill Observatory in Massachusetts, there occurred 

 wave-like fluctuations in the pressure record, which 

 were analyzed by Haurwitz.-^ In these cases upper-air 



data were not sufficiently accurate to compute wave- 

 lengths quantitatively by means of the critical wave- 

 length formula, but it appeared from approximate 

 values of wind shear and density difference that the 

 critical wavelengths might well be occurring. 



If it is desired, then, to predict what wavelengths 

 will occur with a given inversion, the critical values 

 would seem in the light of these observations to give 

 a good estimate of the order of magnitude. 



Assuming that these wavelengths are the ones which 

 occur, one can discuss the velocities and periods of 

 the wave motion. For these critical wavelengths, the 

 velocity of the wave motion is the mean of the veloci- 

 ties of the air masses above and below the inversion. 

 Hence the period can be estimated by dividing the 

 wavelength given in the table by this value. As an 

 example, for a mean velocity of 5 m per second, the 

 periods vary from aliout 6 sec to about 8 min, de- 

 j)ending on the wind shear and density difference. 



The vertical velocity at the inversion cannot be 

 determined, since an arbitrary constant is involved. 

 However, it can be said that this vertical velocity will 

 be reduced to one-tenth its inversion value at a height 

 d equal to 37 per cent of the wavelength above the in- 

 version. This holds strictly only for the incompres- 

 sible, homogeneous case but is approximately correct 

 for the other case as well. 



It is known, then, from theoretical considerations 

 and some observational material, that wave motion is 

 apt to occur at a layer in the atmosphere where there 

 is a temperature inversion accompanied by wind shear. 

 When such inversions are believed to be of impor- 

 tance in affecting the propagation of radio waves, it 

 should be remembered that there may well be wave 

 motion occurring and that the interface is not neces- 

 sarily a level surface. It remains to be determined 

 whether this fact will help to explain the observed 

 very high frequency fading. An estimate of wave- 

 length, period, and velocity of the atmospheric wave 

 motion, as given by Table 13, may be of assistance 

 in testing this possibility. 



*> '^ ANALYSIS OF DUCTS IN THE TRADE 

 WIND REGIONS" 



This report is an analysis of the frequency and 

 magnitude of low-level and elevated ducts as indi- 

 cated by meteorological observations over the trade 

 wind areas of the Atlantic and Pacific Oceans. Mete- 



''By Raymond Waxier, Signal Corps Ground Signal Agency. 



