AbstractDouble‐theodolite observations of pilot balloons were made in trade‐wind air at Anegada (18°45′N, 64°20′W), a small, low‐lying island in the British Virgin Islands, in Spring 1953. Ascents were made at 5 to 15 min intervals over working days of 7 to 8 hr duration on 15 days extending over a total period of 27 days. They provided values of the component air velocitiesu,v,w, in orthogonal co‐ordinate directionsx,y,zrespectively (x,yaxes fixed in horizontal plane,zvertical), over 50 m intervals of height (20‐sec intervals of time) up to about 1·5 km.Fluctuations in the motion at heights up to 1·5 km and of time‐scale varying from about a minute to several days are analysed and discussed. The work is a pioneer study over most of this spectrum and has the special interest of dealing with a field of flow in which the directions of the mean surface wind and the thermal wind are opposed (there was a maximum in the profile of mean wind speed at a height of a few hundred metres) and in which cumulus convection is almost always present.Fluctuations from the mean flow were analysed using averaging periods increasing from about 3 hr up to the whole 27‐day period. For none of these averaging periods was there equipartition of eddying energy in the three velocity components;w′2was one to two orders of magnitude lower thanu′2andv′2, the difference being greater the longer the averaging period.The covariancesu′v′,u′w′,v′w′ were also evaluated for motions at various heights and for the various averaging periods.u′v′ increased with averaging period and changed sign with height: it appeared that horizontal momentum was being transferred to the north by the larger‐scale motions, a smaller amount being transferred to the south by smaller‐scale motions.u′w′ andv′w′ were in general less thanu′v′ and generally varied less systematically with averaging period. Values computed from the smaller components of the motion sampled were in fair agreement with shearing stresses computed by the method of geostrophic departure (using profiles of mean wind and the observed pressure field). The direction of the resultant ofu′w′ andv′w′ agreed surprisingly closely with the direction of the vertical shear vector of the mean wind velocity, the implied coefficient of eddy viscosity for the spectral
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