Asymptotic solutions of an extended Korteweg–de Vries equation describing solitary waves with weak or strong downstream decay in turbulent open‐channel flow. Issue 1 (21st October 2015)

• Record Type: Journal Article
• Authors: Müllner, Markus; Schneider, Wilhelm
• Is Part Of: Proceedings in applied mathematics and mechanics. Volume 15:Issue 1(2015)
• Page Start: 491
• Page End: 492
• Publication Date: 2015-10-21
• Subjects: Applied mathematics -- Periodicals; Engineering mathematics -- Periodicals; Mathematical physics -- Periodicals; 519
• DOI: 10.1002/pamm.201510236
• Languages: English
• ISSNs: 1617-7061

Abstract

Abstract: Solitary waves in turbulent open‐channel flow over a strip of enlarged bottom roughness are considered. Slightly supercritical, fully developed flow far upstream and downstream is assumed. An analysis by Schneider [1] yielded an extended Korteweg–de Vries equation that is solved in the present paper by matched asymptotic expansions up to second order. Solutions for the surface elevation and the location of the wave crest are given. It is shown that a minimum enlargement of the bottom roughness is required for the stationary wave to exist. The surface elevation exhibits either a weak downstream decay, i.e. a shallow 'tail', or, if the enlargement of the bottom roughness equals an eigenvalue, the strong decay of the classical soliton solution. Numerical results available for the latter case [2] are in very good agreement with the present analytical solution. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)