Abstract
In this paper, two-dimensional free surface potential flow over an arbitrary bottom in a channel is considered to analyze the behavior of the free surface profile using linear theory. It is assumed that the fluid is inviscid, incompressible and flow is irrotational. Perturbation analysis in conjunction with Fourier transform technique is employed to determine the first order corrections of some important physical quantities such as free surface profile, velocity potential, etc. From the practical point of view, one arbitrary bottom topography is considered to determine the free surface profile since the free surface profile depends on the bottom topography. It is found that the free surface profile is oscillatory in nature, representing a wave propagating downstream and no wave upstream.
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