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Transcritical Flow Over a Hole
Author(s) -
Grimshaw R. H. J.,
Zhang D.H.,
Chow K. W.
Publication year - 2009
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/j.1467-9590.2009.00431.x
Subject(s) - obstacle , flow (mathematics) , upstream (networking) , nonlinear system , mechanics , computer simulation , physics , geology , mathematics , engineering , geography , telecommunications , archaeology , quantum mechanics
Transcritical flow over a localized obstacle generates upstream and downstream nonlinear wavetrains. In the weakly nonlinear long‐wave regime, this flow has been modeled with the forced Korteweg‐de Vries (fKdV) equation, where numerical simulations and asymptotic solutions have demonstrated that the upstream and downstream nonlinear wavetrains have the structure of unsteady undular bores, connected by a locally steady solution over the obstacle. Further, it has been shown that when the obstacle is replaced by a step of semi‐infinite length, it is found that a positive step generates only an upstream‐propagating undular bore, and a negative step generates only a downstream‐propagating undular bore. This result suggests that for flow over a hole, that is a step down followed by a step up, the two wavetrains generated will interact over the hole. In this paper, this situation is explored by numerical simulations of the fKdV equation.