Variation of Wind with Height in the Upper Layers.— The turbulence produced at the ground only affects the wind distribution in the lowest kilometre or so. Beyond these heights the variations of wind with height are to be ascribed to the horizontal distribution of temperature. For the wind at any level beyond the reach of turbulence will approximate to the geostrophic wind computed from the isobars at that level, and the distribution of pressure at any level depends not only on the distribution of pressure at mean sea level, but also on the distribution of the temperature in the intervening layers. Assuming the wind to be geostrophic mathematical analysis seems to indicate that when there is no horizontal gradient of temperature the wind is at all heights proportional to the absolute temperature. When there is a horizontal gradient of temperature the wind at a level can be derived from the wind at level by first reducing the wind at the lower level in proportion to the absolute temperature, and then adding to it a component blowing around the isobars of mean temperature in the intervening layer, keeping low tempera ture to its left, just as the geostrophic wind blows round the isobars, keeping low pressure to its left. The Computer's Hand book Section ii., Subsection 3, finds the magnitude of the horizon tal temperature gradients corresponding to a given distribution of velocity.
The Transformation of Energy in the Atmosphere by Turbulence.—The effect of the vertical transfer of horizontal momentum by eddies can be represented as a virtual frictional force. Brunt has shown (Phil. Mag., 1926) that the loss of energy of the winds due to turbulence is roughly equal to 5 X kw. per square metre, amounting therefore to the equivalent of a little over 2% of the incoming solar radiation. In the same paper it is shown, with certain assumptions, that if there were no incoming solar energy, the effect of turbulence would reduce the winds to one-tenth their original value in six days. No such annihilation of the atmospheric circulation occurs, and the average conditions persist year after year. The loss of kinetic energy by turbulence is therefore continually compensated by the transformation of roughly 2% of the energy of the incoming solar radiation into kinetic energy. The compensation is not however to be regarded as a process which is always adjusted with precision. It probably proceeds by a kind of trial and error method, and this lack of smoothness must, in part at least, account for the variability of terrestrial weather.
impacts if the free path of a molecule were great when compared with the horizontal displacement of the fluid, a condition which is never satisfied in the portions of the atmosphere accessible to observation of any kind.
It can readily be shown that the left-hand side of equation (3) is usually negligible, and is always small by comparison with gravity. The acceleration 9even in thunderstorms, in which it probably attains its maximum value, never exceeds 5% of the gravitational acceleration. Equation (3) will therefore be re placed by and in equation (I) the term involving the vertical velocity w will be neglected. Since the pressure term is always important, at least one of the other terms must be comparable in magnitude with it. Jeffreys distinguishes three cases.
Eulerian Winds.—Case (i). The rotational and frictional terms are here small by comparison with the accelerational term. The winds satisfying these conditions are called "Eulerian," after Euler, who first found their equations.
Geostrophic Winds.—Case (2). The rotational terms far exceed both the accelerational and frictional terms.
The winds are everywhere along the isobars, with a velocity pro portional to the gradient of pressure and to the secant of the latitude. Jeffreys calls such winds "Geostrophic," following Sir Napier Shaw.
Antitriptic Winds.—Case (3). The frictional terms exceed the rotational and accelerational terms, and the wind is driven by the pressure gradient, but its velocity is limited by friction, provided the journey is sufficiently long. Jeffreys calls these winds "anti triptic" (Gr. Tpm6cs = friction).
In applying this classification Jeffreys reaches the general con clusions that : (a) world-wide phenomena, including the general circulation and its seasonal variation, (b) phenomena on a con tinental scale, including the disturbance of the general circulation in the interior of continents, and (c) phenomena on a scale comparable with the British Isles, including the moving cyclone of temperate latitudes, all satisfy the condition that the rotational terms exceed the accelerational terms, so that they belong to classes (2) or (3) above. To distinguish between the two possible alternatives, Jeffreys appeals to observations of winds, which do not deviate more than four points from the isobar at the surface, and which at a height of a kilometre and above follow closely the direction of the isobars. These winds are thus at least approxi mately geostrophic. In tropical storms, whose average diameter may be taken to be comparable with 8o km., and in which the wind velocities may attain 70 metres per second, the accelerational terms are not negligible, so that the tropical storm is not geo strophic. Since the time of revolution of the tropical storm is only a few hours, while the storm might last for several days, the effect of friction must be relatively small, and the tropical storm, and a fortiori the tornado, must be Eulerian in character.