Theory of waves in the lee of mountains

Abstract The 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 2π/k, small enough for the earth's rotation to be neglected, the stream function of the disturbance satisfies Ψ″ – (g/c 2 +β) Ψ + (gβ/U 2 – U″/U – k 2 ) Ψ = 0(12) Some 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 l must normally decrease upwards, where l 2 = gβ/U 2 – U″/U (13) With two layers, the lower of depth h, these waves can occur if l 1 2 – l 2 2 > π 2 /4h 2 (17) 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 effect 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.