Asymptotic analysis for dispersive fluid filled tubes

Abstract

In a previous paper [J. Acoust. Soc. Am. 64, 522 (1978)] we obtained a new approximate equation governing the propagation of small perturbations to the pressure in a thin-walled fluid filled elastomer tube. There, the spatial fluctuations in the pressure perturbation for fixed time were evaluated numerically by a procedure based on the Fast Fourier Transform (FFT) algorithm. Here, by means of an asymptotic analysis, based on a modified steepest descent method, we explain an apparent anomaly in the numerical results by exhibiting the existence of a forerunner wave and investigate the accuracy of the large time asymptotic results, for times which may be regarded as small or intermediate, by comparing them with the results from the FFT algorithm. It is found that the results obtained from the asymptotic analysis are in close agreement with those obtained from the FFT for moderate times and in qualitative agreement for relatively small times. For nondimensional times greater than 100 the positions of the zeros of the pressure perturbation agreed with those obtained from the FFT to better than four significant figures for the main part of the disturbance.