The Time Periodic Solution of the Burgers Equation on the Half-Line and an Application to Steady Streaming

DOI

10.2991/jnmp.2005.12.s1.24How to use a DOI?

Abstract

The phenomenon of steady streaming, or acoustic streaming, is an important phyical phenomenon studied extensively in the literature. Its mathematical formulation involves the Navier-Stokes equations, and due to the complexity of these equations is usually studied heuristically using formal perturbation expansions. It turns out that the Burgers equation formulated on the half line provides a simple model of the above phenomenon. The physical situation corresponds to the solution of the Dirichlet prolem on the half-line, which decays as x and which is time periodic. We show that the Dirichlet problem, where the usual prescription of the initial condition is now replaced by the requirement of the time periodicity, yields a well posed problem. Futhermore, we show that the solution of this problem tends to the "inner" and "outer" solutions obtained by the perturbation expansions.

Copyright

© 2006, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - A.S. Fokas
AU  - J.T. Stuart
PY  - 2005
DA  - 2005/01/01
TI  - The Time Periodic Solution of the Burgers Equation on the Half-Line and an Application to Steady Streaming
JO  - Journal of Nonlinear Mathematical Physics
SP  - 302
EP  - 314
VL  - 12
IS  - Supplement 1
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2005.12.s1.24
DO  - 10.2991/jnmp.2005.12.s1.24
ID  - Fokas2005
ER  -