Radiation of acoustic and gravity waves and generation of boundary waves in a compressible stratified fluid from a time-varying bottom boundary

摘要

Radiation of acoustic and gravity waves and excitation of boundary waves in a gravitationally stratified isothermal compressible inviscid fluid from a time-varying bottom boundary is investigated. Impedence Z, the ratio of the bottom vertical displacement and fluid pressure above it, is a function of frequency and horizontal wave number (ω, k) of the bottom boundary. The amplitude and phase of Z at the bottom boundary characterize the wavetype generated by the time-varying bottom boundary. Near the acoustic cut-off and the buoyancy frequencies, the amplitude of Z is reduced compared with the cases of the acoustic waves without gravity and incompressible gravity waves. In contract to pure acoustic or gravity wave, the phase of Z is continuous, but changes quickly alogn the regime boundary between the radiating waves and trapped waves in the (ω, k) coordinates, except the Lamb wave branch along which amplitude is zero and across which the phase jumps by π.