Nonlinear Propagation of Acoustic and Internal Waves in a Stratified Fluid

Abstract

The present article is a theoretical study of the combined propagation of acoustic and internal waves of finite amplitude in a (horizontally, say) stratified fluid. The linear theory of small amplitude waves predicts that the two waves (i.e., the fluctuations in acoustic pressure and in vertical particle velocity or displacement) are in general coupled. The waves are decoupled whenever the typical wavenumbers are large compared with the inverse of the scale height for the stratification. Furthermore, a horizontally propagating acoustic wave with zero vertical particle displacement (or velocity), when this is possible, is always decoupled from the internal waves, according to linear theory. In a weakly nonlinear theory, however, the waves may be coupled. A time independent radiation pressure is formed within a standing, horizontally directed acoustic wave, which produces a stationary vertical displacement of the particles. Experimental evidence of this effect has been reported elsewhere [1].