Please use this identifier to cite or link to this item: https://hdl.handle.net/11147/5202
Title: The initial stage of dam-break flow
Authors: Korobkin, Alexandre
Yılmaz, Oğuz
Keywords: Asymptotic analysis
Dam break
Free-surface flows
Matched asymptotic expansions
Issue Date: 2009
Publisher: Springer Verlag
Source: Korobkin, A. and Yılmaz, O. (2009). The initial stage of dam-break flow. Journal of Engineering Mathematics, 63(2-4), 293-308. doi:10.1007/s10665-008-9237-z
Abstract: The liquid flow and the free surface shape during the initial stage of dam breaking are investigated. The method of matched asymptotic expansions is used to derive the leading-order uniform solution of the classical dam-break problem. The asymptotic analysis is performed with respect to a small parameter which characterizes the short duration of the stage under consideration. The second-order outer solution is obtained in the main flow region. This solution is not valid in a small vicinity of the intersection point between the initially vertical free surface and the horizontal rigid bottom. The dimension of this vicinity is estimated with the help of a local analysis of the outer solution close to the intersection point. Stretched local coordinates are used in this vicinity to resolve the flow singularity and to derive the leading-order inner solution, which describes the formation of the jet flow along the bottom. It is shown that the inner solution is self-similar and the corresponding boundary-value problem can be reduced to the well-known Cauchy-Poisson problem for water waves generated by a given pressure distribution along the free surface. An analysis of the inner solution reveals the complex shape of the jet head, which would be difficult to simulate numerically. The asymptotic solution obtained is expected to be helpful in the analysis of developed gravity-driven flows.
URI: http://dx.doi.org/10.1007/s10665-008-9237-z
http://hdl.handle.net/11147/5202
ISSN: 0022-0833
0022-0833
Appears in Collections:Mathematics / Matematik
Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection

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