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Weak Nonlinear Long Waves in Channel Flow with Internal Dissipation
Author(s) -
Yu J.,
Kevorkian J.,
Haberman R.
Publication year - 2000
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/1467-9590.00146
Subject(s) - dissipation , nonlinear system , amplitude , limit (mathematics) , instability , mathematics , flow (mathematics) , wavelength , mathematical analysis , channel (broadcasting) , scale (ratio) , interval (graph theory) , mechanics , internal wave , physics , computer science , telecommunications , optics , quantum mechanics , combinatorics , thermodynamics
This article concerns the evolution of long waves ( O (ε −1/2 ) wavelength) of small [ O (ε)] amplitude in channel flow with internal dissipation. We use multiple scale expansions to derive a generalized Kuramoto–Sivashinsky (GKS) equation that governs the dominant asymptotic solution in the limit of small disturbances and marginal linear instability. We compare this solution with numerical integrations of the full quasilinear system, and show that the error is consistent with an asymptotic solution to ε 3/2 over a time interval of order ε −3/2 .