Nonlinear Theory of Infrasonic Fluctuation Spectra

Abstract

In a previous paper [AGARD Conf. Proc. No. 115 (1972)], the authors have suggested that the 2–5 min period oscillations observed in the ionosphere during periods of thunderstorm activity in the troposphere may be explained in terms of the interaction of the velocity fluctuation fields in thunderstorm regions. This analysis is hem extended to the investigation of the nonlinear interactions of a system of propagating and evanescent internal acoustic-gravity waves. The development rests on Hamilton's principle for nonlinear acoustic-gravity waves with the Lagrangian approximated to third order. The coherent nonlinear interaction problem is discussed with the artifice of two primary waves which interact in a restricted region of space. Although two interacting gravity waves cannot produce a third propagating gravity wave of second order they may produce an acoustic wave in the atmosphere. The general problem of interacting random wave fields is formulated and the evolution of an initially monotonic gravity wave spectrum due to nonlinear interactions is discussed. In addition to affording a possible explanation of the anomalous ionospheric oscillations, the nonlinear interaction theory may explain the well known spectral gap which is found in the kinetic energy spectrum of atmospheric turbulence during periods of convective activity.