Scattering of water waves by a submerged nearly circular cylinder

B. N. Mandal, Sudeshna Banerjea
1995 The Journal of the Australian Mathematical Society Series B Applied Mathematics  
The problem of scattering of surface water waves by a horizontal circular cylinder totally submerged in deep water is well studied in the literature within the framework of linearised theory with the remarkable conclusion that a normally incident wave train experiences no reflection. However, if the cross-section of the cylinder is not circular then it experiences reflection in general. The present paper studies the case when the cylinder is not quite circular and derives expressions for
more » ... ressions for reflection and transmission coefficients correct to order e, where e is a measure of small departure of the cylinder cross-section from circularity. A simplified perturbation analysis is employed to derive two independent boundary value problems (BVP) up to first order in e. The first BVP corresponds to the problem of water wave scattering by a submerged circular cylinder. The reflection coefficient up to first order and the first order correction to the transmission coefficient arise in the second BVP in a natural way and are obtained by a suitable use of Green's integral theorem without solving the second BVP. Assuming a Fourier expansion of the shape function, these are evaluated approximately. It is noticed that for some particular shapes of the cylinder, these vanish. Also, the numerical results for the transmission coefficients up to first order for a nearly circular cylinder for which the reflection coefficients up to first order vanish, are given in tabular form. It is observed that for many other smooth cylinders, the result for a circular cylinder that the reflection coefficient vanishes, is also approximately valid. 'Physics and Appl. Math. Unit,
doi:10.1017/s0334270000010481 fatcat:572sjbvvsbehtbnc4ior44izcq