Electron. J. Diff. Equ., Vol. 2016 (2016), No. 190, pp. 1-8.

A waveless free surface flow past a submerged triangular obstacle in presence of surface tension

Hakima Sekhri, Fairouz Guechi, Hocine Mekias

Abstract:
We consider the Free surface flows passing a submerged triangular obstacle at the bottom of a channel. The problem is characterized by a nonlinear boundary condition on the surface of unknown configuration. The analytical exact solutions for these problems are not known. Following Dias and Vanden Broeck [6], we computed numerically the solutions via a series truncation method. These solutions depend on two parameters: the Weber number $\alpha$ characterizing the strength of the surface tension and the angle $\beta$ at the base characterizing the shape of the apex. Although free surface flows with surface tension admit capillary waves, it is found that solution exist only for values of the Weber number greater than $\alpha_0$ for different configurations of the triangular obstacle.

Submitted November 5, 2015. Published July 13, 2016.
Math Subject Classifications: 35B40, 35Q35, 76B07, 76D45, 76M40.
Key Words: Free surface; potential flow; Weber number; surface tension; nonlinear boundary condition.

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Hakima Sekhri
Department of Mathematics, Faculty of sciences
University Setif1.19000, Algeria
email: sekhrihakima@yahoo.fr
Fairouz Guechi
Department of Mathematics, Faculty of sciences
University Setif1.19000, Algeria
email: f_guechi@yahoo.fr
Hocine Mekias
Department of Mathematics, Faculty of sciences
University Setif1.19000, Algeria
email: mekho58@gmail.com

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