The Origin of Cyclones of Middle Latitudes

THE ORIGIN OF CYCLONES OF MIDDLE LATITUDES The Convection Theory.—The so-called convection theory of the origin of cyclones supposes that thermal causes produce a strongly localized ascending current in one place, and that the convergence of air from the surrounding regions to take the place of the air removed by the ascending current brings into existence a circulation of winds round the centre, in the counter clockwise direction. The resulting cyclone is effectively to be regarded as a disc of revolving fluid. The nature of the cir culations produced when fluid is removed from a disc of fluid revolving with a constant angular velocity was first given by Rayleigh (Proc. Roy. Soc. A., vol. xciii.) who showed that the resulting transverse velocity v at distance r from the centre is given by the equation where B is proportional to the amount of fluid removed. It was shown by Brunt (Proc. Roy. Soc. A., vol. xcix.) that the original velocity of rotation might be merely the rotation of the air with the earth, in which case the subsequent motion relative to the earth became Thus intense localized convection in air originally still should give rise to a cyclonic circulation, provided it is possible for the air which rises to be carried away from the region in question, so as to provide for the diminution of pressure at the centre. The most obvious method of removal of the ascended air is by means of a strong current in the upper air. It is readily seen that unless there is somewhere in the upper air a current suffi ciently strong to carry the ascended air quickly away from the region of ascent, there is no possibility of forming a cyclone. For if air is removed vertically from the lower layers, there is a converging flow of air from the surrounding region to take the place of the air removed, and the net result will be to increase the pressure over the region. This in turn will set up a pressure gradient opposing the inward motion, and must rapidly check the motion of convergence.

On this theory the cyclone consists of a column, or rather of a disc of revolving fluid, rotating about the centre of lowest pressure, and having a system of circular isobars. If the con vection is set up in a moving current, the cyclone has the general motion of the current (Shaw, Geophysical Memoir No. 12 and Proc. Roy. Soc. A., 1917). This theory and some of its conse quences have been discussed in some detail by Sir Napier Shaw in The Air and its Ways.

Shaw describes the cyclone as originating in the ascent of a mass of air which is lighter than its surroundings. The ascending mass of air has no inviolable boundary, and as it rises through its environment the turbulent motion set up at its boundaries causes a partial mixing with the environment, with the result that an increasing mass of air has its temperature raised above that of its immediate environment. This process is called the "evic

tion" of air.

The Polar Front Theory.

Dove developed in some detail the idea that a cyclone could be regarded as a region of opposition of warm and cold currents, and a number of later writers sup ported this same view. The work of Shaw and Lempfert (Shaw, Forecasting Weather, chap. 7) in the Life History of Surface Air Currents led them to the view that the air currents in a cyclone could be represented diagram matically by fig. 5, and that the rain which fell in the cyclone could be explained by the forced ascent due to convergence, or by the ascent of warm air over cold air.

Later V. Bjerknes combined this picture of the cyclone with the ideas of Helmholtz. The latter had shown that it was possible for two currents of different temperatures and different velocities to flow side by side, separated by a surface of discontinuity, the arrangement being entirely stable. Bjerknes ("The Dynamics of the circular vortex," etc., Geofysiske Publikationer, Oslo, vol. ii.

No. 4 and "The Structure of the Atmosphere When Rain Is Fall ing," Q.J.R. Met. Soc., 1920) suggested that the cyclone should be visualized as a wave on the surface of separation between cold easterly currents of polar origin, and warm westerly currents of equatorial origin. The cold air of polar origin is called "polar air," and the warm air of equatorial origin "equatorial air," while the surface of sep aration is known as the "polar front." The theory put forward by Bjerknes, the "po lar front" theory, has not yet been fully developed. To begin with, the develop ment of waves in an inclined surface of separation has not been treated with math ematical precision. The whole question of the exact processes involved in the pro duction of cyclones at a polar front bristles with theoretical difficulties. The polar front is only inclined at a very small an gle (1° to 1 °) to the horizontal plane. Bjerknes regards the waves which form at the polar front as gravitational waves, and he suggests that the effect of the earth's ro tation will be to increase the extent of the horizontal deviations, so that they become enormously greater (instead of much less) than the vertical displacements. The waves increase in amplitude, and a cyclone sometimes forms at the northern crest of a wave. This theory is strongly reminis cent of Emden's theory of sun spots (Gaskugeln, 1907). As put forward by Bjerknes it presents numerous gaps, and the argument is of a general character.