Elements

The Nature of Wind. Turbulence.

On account of fric tion at the surface of the earth the air is always in turbulent mo tion, eddies being formed in much the same way as in a stream of water moving over an uneven bed. The pattern of the eddies is made visiblp by smoke from a chimney or other fire, but the fact that the motion of air is not steady motion is clearly shown by any anemometer chart on which the instantaneous velocity or direction of the wind differs considerably from the mean value over an interval of time. Since eddies formed in an air current are of finite size they must cause mixing of adjacent layers of air, and they therefore act as agents in diffusing momentum, heat, water vapour, dust, carbon dioxide, and other properties or constituents of the atmosphere.

G. I. Taylor (Phil. Trans. A, 1915) showed that the power of eddies for diffusing momentum, heat, or other constituents, may be represented by a constant K, the eddy diffusivity, which is roughly proportional to iwd where w is the mean vertical com ponent of velocity in the eddies, and d the mean diameter of the eddies. The value of K on any particular occasion will depend upon a number of factors, notably the nature of the surface of the ground and the lapse rate of temperature. Values of K have been estimated varying from 3X c.g.s. units in inversions over the Great Banks of Newfoundland, to over Paris.

The theory elaborated by Taylor gives the flow of heat, etc. across unit area of a horizontal plane, moving with the mean motion of the air. This mean motion will depend upon the size of the area over which the mean is taken, since in the atmosphere there are eddies of widely varying sizes. The value of K which we adopt in a particular problem should therefore be a function of the size of the parcel of air with which we are concerned.

Taylor has approached the problem from a different standpoint in a paper in Proceedings London Mathematical Society 1921. Richardson (Phil. Mag., 1925) has discussed the relation which must subsist between the vertical gradients of temperature and wind if turbulence is to increase. Richardson has also given a more general treatment of the question of turbulence, allowing for the possibility of K varying with height (Proc. Roy. Soc. A, 1919). In this connection see also a paper by Jeffreys in Proc. Camb. Phil. Soc., 1929. An extension of these ideas to the general circulation, treating the cyclones and anticyclones as eddies, has been given by Defant Geografiska Annaler, 1921. A useful sum mary of the work of Richardson, Taylor and others is given by C. G. Rossby (Monthly Weather Review, 1927). The effect of

turbulence upon evaporation from large sheets of water has been discussed by Giblett (Proc. Roy. Soc., 1921) and Angstrom (Archie. for Mat. Astr. och Fysik, 1921).

The Variation of Wind with Height in the Lowest Lay. ers.—If in fig. 4, 0 G represents the geostrophic wind G in mag nitude and direction, and 0 P the wind at height z in magnitude and direction, then P sweeps out an equiangular spiral, and the line OS, representing the surface wind, is a tangent to this spiral. The spiral summarizes the distri: bution of wind with height in a convenient form. It attains the geostrophic velocity at a lower height than the geostrophic wind direction, and as was shown by G. I. Taylor (Q.J.R. Met. Soc., 1914), this fits the observed facts with reasonable accuracy. The geostrophic wind should give a good approximation to the actual conditions at a height of about I km. It follows that the effect of turbulence due to the ground only extends to heights of 500-1 ,00o metres.

Taylor's treatment of turbulence in terms of a coefficient K which is assumed to be independent of height thus enables us to account for the general nature of the variations of wind and temperature in the lower layers of the atmosphere, though the uncertainty as to the contribution of direct radiation and ab sorption to the temperature changes, renders uncertain any estimate of K from the temperature variations alone. The use of Taylor's coefficient K has led to a clearer physical understanding of the processes associated with turbulence in the atmosphere, yet it is certain that no theory at present available is capable of ex plaining all the facts. In this connection see also papers by L. F. Richardson in Memoirs R. Met. Soc. vol. i. No. 1, and Proc. Roy. Soc. A, 1926.

A theoretical discussion of the form of clouds of smoke emitted from point and line sources, based on an extension of Taylor's method of treatment, has been given by 0. F. T. Roberts in Proc. Roy. Soc. A, 1923. The subject of turbulent motion in the atmosphere has been discussed by Schmidt in a number of papers published in the Sitzungberichte d. Wiener Akad. d. Wiss. from 1917 onwards, by Sverdrup in papers in the publications of the Geophysical Institute, Leipzig, and elsewhere, and by Hessel berg in Geofisiske Publ. vol. iii. A discussion of this and many kindred subjects, together with full references to the work of English and Continental writers will be found in Weather Pre diction by Numerical Process by L. F. Richardson, 1922.