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We study the flow of water waves over bathymetry that varies periodicallyalong one direction. We derive a linearized, homogenized model and show thatthe periodic bathymetry induces an effective dispersion, distinct from thedispersion inherently present in water waves. We relate this dispersion to thewell-known effective dispersion introduced by changes in the bathymetry innon-rectangular channels. Numerical simulations using the (non-dispersive)shallow water equations reveal that a balance between this effective dispersionand nonlinearity can create solitary waves. We derive a KdV-type equation thatapproximates the behavior of these waves in the weakly-nonlinear regime. Weshow that, depending on geometry, dispersion due to bathymetry can be muchstronger than traditional water wave dispersion and can prevent wave breakingin strongly nonlinear regimes. Computational experiments using depth-averagedwater wave models %, as well as confirm the analysis and suggest thatexperimental observation of these solitary waves is possible.

Solitary water waves created by variations in bathymetry