Distortion of Wave-Form of Weak and Short Wave in Eulerian Fluid

Abstract

The distortion of wave-form of a wave propagating in Eulerian fluid is studied theoretically. The geometrical acoustics is applied for the weak and short wave. The displacement vector of the wave is assumed to be a product of the amplitude vector and the waveform which is a function of eikonal. The amplitude, the wave number and the frequency are assumed to vary gradually. From the first approximation of the equation of motion, the existence of a longitudinal wave is proved and the propagation velocity is obtained. From its second approximation, the evolutional equation of amplitude is reduced. By that equation, the distortion of the wave-form is analyzed. It may be flatter or steeper according to the material function, the curvature of the wave-form and the direction of the displacement of the wave.