Generation of Internal Gravity Waves in the Thermosphere during Operation of the SURA Facility under Parametric Resonance Conditions

Gennadiy I Grigoriev,Elena E Kalinina,Victor G Lapin

doi:10.3390/atmos11111169

Abstract

The problem of excitation of internal gravity waves (IGWs) in the upper atmosphere by an external source of a limited duration of operation is investigated. An isothermal atmosphere was chosen as the propagation environment of IGWs in the presence of a uniform wind that changes over time according to the harmonic law. For the vertical component of the displacement of an environment, the Mathieu equation with zero initial conditions was solved with the right part simulating the effect of a powerful heating facility on the ionosphere. In the case of a small amplitude of the variable component of the wind, the time dependence of the vertical displacement under parametric resonance conditions using the perturbation method is obtained. The obtained dependence of the solution of the differential equation on the parameters allows us to perform a numerical analysis of the problem in the case of variable wind of arbitrary amplitude. For practical estimations of the obtained values, data on the operating modes of the SURA heating facility (56.15° N, 46.11° E) with periodic (15–30 min) switching on during of 2–3 h for ionosphere impact were used.

Highlights

Internal gravity waves are one of the main components of the ionosphere dynamics
Since the Mathieu Equation (2) describes the mechanism of parametric resonance [14], we will answer the question whether it is possible to increase the efficiency of the impact on the environment for the accepted model at a fixed power of the transmitter
Consider the source in the form of an exponentially decreasing cosine over time f1 (t) = exp(−αt) · cos(ω1 t + φ) · θ(t). The duration of this source is limited by a parameter α, the beginning of the source action is determined by the Heaviside step function θ(t) = 1 for t > 0, θ(t) = 0 for t < 0 and the source phase φ has a strong influence on the solution

Summary

Introduction

IGWs are studied using many methods including either measuring of parameters of the neutral or the ionized component of the atmosphere. It seems plausible that the operation of powerful facilities can lead to a noticeable and controlled impact on the environment, the results of which are recorded by modern techniques. This problem is discussed in more detail in the reviews [9,10]. IGW parameters are determined on the basis of measuring the altitude-temporal variations of the electron concentration, temperature and density of the neutral atmosphere, and the velocity of vertical plasma motion by the method of creating artificial periodic irregularities [9,10]. Mechanisms of transformation of this power into heat and the part of it that is carried away from the impact area by various physical processes need to be investigated

Problem Statement

Problem Solution

Dependence the amplitude displacement onφ phase

Numerical Estimation

Conclusions