Theoretical studies of shock waves in nonlinear, dispersive and dissipative media
2004 (English)In: Acta Acoustica united with Acustica, ISSN 1610-1928, Vol. 90, no 4, 662-678 p.Article in journal (Refereed) Published
Propagation of waves in nonlinear, dispersive and dissipative media, as described by Korteweg-de Vries-Burgers' equation (KdVB), have been studied. The focus of the investigation has been to study analyticaly, the structure of a shock wave that is broken down by dispersive and dissipative phenomena. To be able to use the inverse scattering transform (IST) to get analytical solutions for Korteweg-de Vries' equation (KdV), an N-wave was used as model for the initial shock. The IST is used to transform KdV, which is a nonlinear differential equation, into Marchenko's equation that is a linear Volterra integral equation. A zeroth order iteration solution, which reconstructs the initial waveform, is presented. For positive times, this solution shows a decaying shock front which slows down, leaving an oscillating tail behind. In the early stages, the behaviour of the leading and the tailing shock of the N-wave are similar but soon the structure caused by the tailing shock is disrupted by the oscillating tail of the leading shock. This solution is valid for moderate values of the dispersion coefficient. In order to obtain solutions for smaller values of the dispersion coefficient, asymptotic analysis is used. The corresponding asymptotic analysis for Burgers' equation, with a small dissipation coefficient, is quoted for comparison. An asymptotic analysis is also made for KdVB, in the case for which dispersion as well as dissipation is important.
Place, publisher, year, edition, pages
2004. Vol. 90, no 4, 662-678 p.
IdentifiersURN: urn:nbn:se:kth:diva-41255ISI: 000223441700010ScopusID: 2-s2.0-4243191476OAI: oai:DiVA.org:kth-41255DiVA: diva2:443302
QC 20110923. Stockholm Music Acoustics Conference (SMAC 03). Stockholm, SWEDEN. AUG 06-09, 2003 2011-09-232011-09-232011-10-18Bibliographically approved