Amplitude equations for a linear wave equation in a weakly curved pipe
Abstract
We study boundary effects in a linear wave equation with Dirichlet type conditions in a weakly curved pipe. The coordinates in our pipe are prescribed by a given small curvature with finite range, while the pipe's cross section being circular. Based on the straight pipe case a perturbative analysis by which the boundary value conditions are exactly satisfied is employed. As such an analysis we decompose the wave equation into a set of ordinary differential equations perturbatively. We show the conditions when secular terms due to the curbed boundary appear in the naive peturbative analysis. In eliminating such a secularity with a singular perturbation method, we derive amplitude equations and show that the eigenfrequencies in time are shifted due to the curved boundary.
Cite
@article{arxiv.0910.0549,
title = {Amplitude equations for a linear wave equation in a weakly curved pipe},
author = {Shin-itiro Goto},
journal= {arXiv preprint arXiv:0910.0549},
year = {2015}
}
Comments
To appear in J Phys A: Math. Theor