Propagation of surface waves on a background shear flow with constantvorticity is studied and compared against the case when the background flow isuniform in depth. For a shear flow with the linear vertical profile, thedispersion relation of surface gravity waves is minutely analyzed for a fluidof finite depth. Under the assumption that the background flow gradually variesin the horizontal direction, the primary attention is paid to the wave blockingphenomenon; the effect of vorticity on this phenomenon is studied in details.The conditions of wave blocking are obtained and categorized for differentvalues of the governing dimensionless parameters.
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