THE FAR-FIELD OF A MOVING OSCILLATING SOURCE IN THE CASE OF RESONANCE

The field excited by a moving oscillating source in a two-dimensional linear medium with dispersion (for example, a source of surface waves) is considered. It is assumed that the velocity of the source is equal to the group velocity corresponding to its oscillation frequency (tak ing the Doppler shift into account), i.e, resonance occurs. The asympt otic form of the wave field in the far zone for long time t is describ ed. In particular, in the neighbourhood of the zero there is a resonan ce zone in which the wave field is of the order of unity or higher and the size of which increases as t(2/3) in critical directions, i.e. in directions perpendicular to the dispersion curve at its point of self -intersection. In directions which differ from the critical direction, the size of the resonance zone increases as t(1/2). The case of a deg enerate stationary point of the dispersion function is also considered . A sharper resonance then occurs and the field increases as t(1/6). T he three-dimensional problem is briefly considered. (C) 1998 Elsevier Science Ltd. All rights reserved.