Theory of non‐horizontal adiabatic flow in the atmosphere

The equation of continuity takes the form when there are appreciable vertical displacements (see Section 1 for list of symbols). The stream function, Φ, for two‐dimensional steady motion satisfies an equation which for vertical displacements of less than about a kilometre reduces to the form where G 1 and G 2 are functions of Φ determined by the profile of the air current entering the region under study. This is probably the best form for numerical solution. Bernoulli's equation shows that ( gz + q 2 – τ) is constant along a streamline in steady adiabatic flow. The perturbation equations which have already been widely used are derived as a special case. Except in this case the solution for three‐dimensional flow is very much more difficult to obtain than that for two‐dimensional flow. The lateral stretching of vortex lines in flow over unlevel ground reduces or increases the surface wind according as the wind increases or decreases with height. This process may be used to explain the location of blow‐downs in forests on hillsides. The generation of shear in non‐horizontal motion can occur at already existing discontinuities of temperature (or velocity). If the motion is unstable so that turbulence is generated, other things being equal the more stable (statically) the temperature inversion the more likely it is to produce turbulence in mountain waves.