## Abstract

This paper describes an observational study of the mean and larger-scale turbulent structure of the wind in the lowest 1500 m of the North-East Trades. The observed motions are used both alone and in conjunction with the horizontal pressure field to deduce values of the vertical transport of momentum; the pattern of cumulus cloud convection is borne in mind throughout. Sections 1 and 2 provide a brief survey of the background to the expedition and of the simplified equations by which the observations are interpreted. Section 3 describes the site and observations in detail. 466 double-theodolite pilot-balloon soundings were made in the spring of 1953 from the small flat island of Anegada (18 degrees N, 64 degrees W). Soundings were made on 15 days over a 27-day period, balloons being released at intervals of 5 to 15 min. The balloons, rising at about 150 m/min, were observed every 20 s for 9 min, to obtain the three components of the motion in 50 m layers over the lowest 1350 m. Special observations of pressure were made in a network of neighbouring islands. The derivation of component air velocities and of the horizontal pressure gradient as a function of height is described in section 4. Difficulty was experienced in obtaining the pressure field with requisite accuracy. Surface observations of the weather in relation to the main aim of the study are discussed in section 5. The mean angle between surface wind and isobar over the 15-day period was 13 degrees, notably less than the climatological value of about 33 degrees. Section 6 discusses the properties of the mean horizontal motion for the whole period of observation. The easterly component of wind velocity was greatest at 350 m, and the wind veered with height through 24 degrees in the first 1350 m. There was also a veer of geostrophic wind in this layer of about 13 degrees so that some down-gradient motion remained at the top of the layer. It is shown that the mean values of the local and advective components of acceleration were negligible compared with others terms in the momentum balance. Section 7 uses the wind profiles of section 6 together with the mean horizontal pressure field to find the distribution of shearing stress with height, assuming that ageostrophic flow is balanced by internal friction. The mean stress in the direction of the surface wind varied from 0$\cdot $41 dyn/cm$^{2}$ at the surface to -0$\cdot $37 dyn/cm$^{2}$ at 1300 m. The former provides a coefficient of surface stress, based on the anemometer windspeed, c = 1$\cdot $5 $\times $ 10$^{-3}$. The mean stress in the direction normal to the surface wind varied from zero (assumed) at the surface to 0$\cdot $17 dyn/cm$^{2}$ at 200 m, and was small above 800 m, but internal consistency is only obtained by assuming the horizontal gradient of temperature near the surface to be appreciably greater than the climatological value for the general area. The stresses and related gradients of mean motion imply eddy viscosities of order 10$^{5}$ cm$^{2}$/s throughout the layer. Section 8 discusses the vertical profiles of daily mean wind, which are variable from day to day. It was not possible to analyze the profiles to find shearing forces because of uncertainty in the acceleration terms, and in the pressure field. Section 9 is concerned with the analysis of fluctuations of wind at heights up to 1350 m, using averaging periods increasing from about 3 h up to the whole 27-day period. For none of these averaging periods was there equipartition of eddying energy in the three velocity components; $\overline{w^{\prime 2}}$, the vertical intensity, was one to two orders of magnitude lower than $\overline{u^{\prime 2}}$ and $\overline{v^{\prime 2}}$, the horizontal intensities, the difference being greater the longer the averaging periods. The covariances $\overline{u^{\prime}v^{\prime}}$, $\overline{u^{\prime}w^{\prime}}$ and $\overline{v^{\prime}w^{\prime}}$ were also evaluated for various heights and averaging periods. $\overline{u^{\prime 2}}$, $\overline{v^{\prime 2}}$ and $\overline{u^{\prime}v^{\prime}}$ increased with averaging period and from their variation crude estimates are made of lag covariances which are equivalent to spectra. Values of $\overline{u^{\prime}v^{\prime}}$ for the larger components of the motion sampled were in fair agreement with those of early workers. $\overline{u^{\prime}w^{\prime}}$ and $\overline{v^{\prime}w^{\prime}}$ were in general less than $\overline{u^{\prime}v^{\prime}}$ and did not vary systematically with averaging period. The values for the smaller scale components of the motion sampled were in fair agreement with shearing stresses computed by the method of geostrophic departure (section 7). The direction of the resultant of $\overline{u^{\prime}w^{\prime}}$ and $\overline{v^{\prime}w^{\prime}}$ agreed surprisingly well with the direction of the vertical shear vector of the mean wind velocity, the implied coefficient of eddy viscosity for the spectral range sampled again being about 10$^{5}$ cm$^{2}$/s over the whole range of height. An appendix considers the effect of the island, about 30 km$^{2}$ in area, on the oceanic Trades; the land was strongly heated by the sun and a particular pattern of convective cloud was usually set up. The associated field of mean vertical motion, of the order of 10 cm/s, and the disturbance of the field of horizontal mean motion have been partly evaluated. It is found that the velocities measured on the upwind shore were fairly representative of those over the open ocean, even though slow steady rising and sinking motions were detected.