Sound and light propagation in a weakly inhomogeneous atmosphere

Small-scale inhomogeneities caused by atmospheric turbulence have a considerable effect on sound and light propagation, producing the fluctuations of these wave fields. V A Krasilnikov 1, 2] performed experiments on phase and amplitude variations of a sound wave propagating through the atmosphere. Fluctuations of light-wave parameters occur, for example, in the well known phenomenon of star scintillation, apparently strongly connected with turbulent irregularities of the atmospheric temperature field 3, 4]‡.

Some calculations of phase (arrival angle) and amplitude fluctuations for a wave propagating through a turbulent medium are described by Krasilnikov 1, 3, 8]. All these and similar calculations are based on the geometrical optics (acoustics) approximation, which may be the reason for disagreement between calculation and experimental data in some cases. Thus, for example, amplitude fluctuations in the geometrical approximation turn out to be proportional to the distance of propagation through a turbulent medium to the power of 3/2. However, observations usually show much slower fluctuation growth.

This paper represents an attempt to consider the problem of amplitude and phase variations for a scalar wave field in terms of more general equations including some diffraction effects. Incidentally, the range of validity of geometrical optics theory becomes clear.