The propagation of a pulse in the atmosphere

Abstract

In a recent paper (Pekeris 1937) it has been shown that under certain assumed temperature distributions above 35 km. the atmosphere is found to have a period of free oscillation of nearly 12 solar hours. In this mode of oscillation, which will be referred to as the second mode, the pressure variations above and below 30 km. are in opposite phase. There is also another mode of free oscillation (the first mode) of a period of about 10 1/2 hr., in which there is no reversal of phase in the pressure variation. A free period of 12 solar hours is required by Kelvin’s “resonance” theory of the semidiurnal variation of the barometer and the reversal of phase as well as the large amplitudes at great heights of the pressure variation in the second mode are in accordance with the interpretation of diurnal variation of the earth’s magnetic field by the “dynamo” theory (Chapman 1934). There is additional evidence about the free modes of oscillation of the atmosphere from the propagation of long waves, since, according to a theorem of G. I. Taylor (1936) there corresponds to every free mode a definite speed of long waves. Now the atmospheric wave which was caused by the Krakatoa eruption in 1883 travelled with a speed corresponding to the first mode, and the question arises whether the apparent lack of a second wave in the Krakatoa disturbance is evidence against the existence of the second mode. Qualitatively, it can be argued that a volcanic eruption which takes place at the ground would excite a higher amplitude in the first mode because in it the energy distribution is more concentrated toward the ground than in the second mode. This would follow from the general dynamical principle that one cannot excite a free mode by applying a pulse at a nodal point, as is strikingly manifested by the fact (Stoneley 1931) that the deeper the focus of an earthquake the smaller are the amplitudes of the surface (free) waves.