We consider the classic Lagrange long gravitational wave of a homogeneous incompressible
fluid in a shallow canal with a corrugated bottom. We use the asymptotic expansion method
to find the effective depth of a one-dimensional canal and, hence, the effective wave velocity.
A flow in a two-dimensional tank with a corrugated bottom is also studied by this method.
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Dingemans M.W., 1997, Water Wave Propagation Over Uneven Bottoms, Part 1 – Basic Equations, Part 2 – Wave propagation formulation, Advanced Series on Ocean Engineering: Vol. 13, World Scientific, Delft.
Evangelos K., 2012, The impact of vegetation on the characteristics of the flow in an inclined open channel using the piv method, Water Resources and Ocean Science, 1, 1, 1-6.
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Mei C.C., Vernescu B., 2010, Homogenization Methods for Multiscale Mechanics, World Scientific Publishers, New Jersey-London-Singapore-Beijing-Shanghai-Hong Kong-Taipei-Chennai.
Wojnar R., Bielski W., 2014, Flow in the canal with plants on the bottom, [In:] Complex Analysis and Potential Theory with Applications, T. Aliev Azerogly, A. Golberg, S.V. Rogosin (Edit.), Cambridge Scientific Publishers, 167-183.
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