Free surface flow over an obstacle. Theoretical study of the fluvial case

Abstract

The two-dimensional stationary flow of a fluid over an obstacle lying on the bottom of a stream is discussed. We take into account the gravity and we neglect the effects of the surface tension. An existence theory for the solution of this problem is established by the implicit function theorem, for small obstacles and Froude numbers in an interval included in $\left]0,1\right[$.