Instability in the oscillations of a moving oscillator while it radiates surface and internal waves

Abstract

In the study of wave radiation by oscillators moving in a fluid considerable interest attaches to the question of the effect which the radiation has on the nature of the motion of the source. The main task here is to clarify the conditions under which the component of the radiation reaction force connected with the radiation of anomalous Doppler harmonics prevails over the component of the reaction force in the region in which normal Doppler frequencies are radiated. The latter results in a buildup in the oscillations of an oscillator moving in a dispersing medium [1, 2]. In the present study the authors obtain in the dipole approximation expressions for the reaction force of radiation (wave resistance) of a mass source of the oscillator type [2] when it excites surface waves in an incompressible fluid of finite depth, and internal waves in a smoothly stratified fluid. The thresholds are also found for the occurrence of radiation instability with respect to gravitational waves, and is found that with respect to internal waves radiation instability is nonthreshold in character in the Boussinesq approximation.