SUMMARYThe disturbance in an air current, whose velocity may vary with height, caused by irregularities in the ground, is obtained. For a wave-like corrugation of the ground of wavelength m / k , small enough for the earth's rotation to be neglected, the stream function of the disturbance satisfiesSome circumstances in which waves may have large amplitude only in the lower layers of the atmosphere are described. In order that such waves may occur over level ground in the lee of mountains the parameter 1 must normally decrease upwards, where With two layers, the lower of depth h, these waves can occur if Fourier's integral theorem is used to obtain the flow in two instances. Fig. 3 shows the wave due to a single long ridge in a stream in which the wind is stronger at higher levels. Fig. 5 shows the flow of a shallow current descending from a plateau, the air being calm above.Nodal surfaces, as in Fig. 5, occur only when the depth of the layer exceeds a critical value, depending on the details of wind speed and temperature.The well-known cloud phenomena associated with the waves are briefly described in section 6, and in section 7 the eRect of isolated mountains rather than long ridges is considered.The theory is only valid for streamline, dry, isentropic, inviscid flow in which the disturbance is only a small proportion of the wind velocity.

Isolated masses of buoyant fluid were released in a water tank. Their width, 2r, and the distance travelled, z, were measured as functions of time and were found to follow roughly the laws $r = nz,\;\;\;\;\; w = C(g \overline {B}r)^ \frac{1}{2},$ where w is the vertical velocity, $\overline {B}$ the mean buoyancy, and n and C are constants. These equations are predicted by dimensional analysis, assuming viscosity to be negligible, and the constants appear to be independent of the Reynolds number. It is found that C [eDot ] 1·2 and n is in the neighbourhood of 4.Since the Froude number relating the buoyancy and inertia forces is the same as for isolated masses of buoyant air in the atmosphere, it is concluded that the constants will have the same value in this latter case. This is confirmed roughly by observation of cumulus cloud towers.Some of the characteristics of the motion observed in the experiments are described and comparison is made with vortex rings.

SUMMARYThe process of convection is described in terms of a unit or proton of convection -the bubble. A rising bubble of warm air sheds its outer skin steadily into a disturbed wake until it becomes exhausted completely or spreads out at a stable layer. The wake is a region where the ascent of further bubbles is favoured. The wakes of small bubbles close to the ground are aggregated into larger bubbles, which are more dilute, up to a level where they begin to penetrate hitherto undisturbed air, and then they waste away as they ascend further.The air above a bubble is lifted (and cooled) as the bubble approaches and then drains down the outside, the air close to the bubble being mixed into the wake. The wake of a clear bubble is buoyant but that of a cloudy bubble may sink if it is sufficiently chilled by dilution with surrounding clear air.The drag on a bubble is estimated from observations on rising cumulus towers, and a linear relation between buoyancy and limiting velocity is proposed. From this the horizontal velocity of the bubble relative to the surrounding air is deduced to be about the same as the vertical velocity when it ascends through strong shear.A bubble is a compact stable configuration for a rising element. Near the ground the heat is transported by small bubbles, which are less efficient, and therefore require a greater lapse rate, than the larger ones which can operate higher up. The process of aggregation is again renewed within large clouds so that the bubbles found at the top may be more dilute than if they had ascended directly from the base. Clouds growing in a shearing current will grow into the shear.