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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 |
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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