Increased attention is currently paid to studying the so-called "secondary" acoustic-gravity waves (AGWs), which appear due to instabilities and nonlinear interactions of "primary" wave modes generated by atmospheric sources. This report is devoted to the study of horizontal spatial spectra of primary and secondary AGWs at fixed altitude levels in the middle and upper atmosphere using a high-resolution three-dimensional nonlinear model AtmoSym. It is found that in a short time after turning on the source of plane waves at the lower boundary of the model, the spectrum contains mainly a peak related to the primary AGW. Later, spectral peaks corresponding to secondary AGWs appear at horizontal wave numbers that are multiples of the wave numbers of the primary wave. This study allows estimating relative contributions of secondary AGWs at different heights, different times, and for different atmospheric conditions.
A high-resolution three-dimensional numerical model is used for studying nonlinear acoustic-gravity waves (AGWs), propagating from the Earth's surface into the upper atmosphere. Wave sources contain the superposition of two AGW harmonics with different periods, wavelengths and phase speeds. Large-scale AGWs change background conditions for the propagation of smaller-scale wave modes and can modulate their amplitudes. Simulations showed that nonlinear interactions might create small-scale structures in the upper atmosphere. Largest amplitudes of temperature disturbances occur at altitudes 100 – 200 km, producing convective instabilities at altitudes 100 – 120 km. Largest wave-induced increases in the mean temperature exist at altitudes 100 – 150 km. Above 200 km, changes in the mean temperature are mainly negative for the smaller-scale wave mode and are positive for the larger-scale mode and for their superposition. Interactions of two waves propagating in opposite directions produce the mean flows directed opposite and along the x-axis at different altitudes. Simulated wave-induced changes in the mean temperature and horizontal velocities produced by wave sources composed of two wave modes in the nonlinear model are different from the sums of respective changes created by the individual modes. These differences show that nonlinear interactions may significantly influence dynamical and thermal effects produced by sets of AGW spectral modes propagating in the atmosphere.
The propagation of X-ray waves through an optical system consisting of 33 aluminum X-ray refractive lenses
is considered. For solving the problem, a finite-difference method is suggested and investigated. It is shown
that very small steps of the difference grid are necessary for reliable computation of propagation of X-ray waves
through the system of lenses. It is shown that the wave phase is a function very quickly increasing with distance
from an optical axis, after the wave has propagated through the system of lenses. If the phase is a quickly
increasing function, then the wave electric field is a quickly oscillating function. We suggest and recommend
using the equation for a phase function instead of the equation for an electric field. The equation for a phase
function is derived.
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