A hydraulic jump is a physical phenomenon commonly observed in nature such as in open channel flows or spillways and is dependent upon the relation between the initial upstream fluid speed and a critical speed characterized by a dimensionless number F known as the Froude number. In this paper we prove the existence of hydraulic jumps for stationary water-waves as a consequence of the existence of bifurcation branches of non-flat liquid interfaces originated from each of a sequence of upstream velocities F1 > F2 > ⋯ > Fr > ⋯ (Fr → 0 as r → ∞). We further establish explicitly, for F > 0, F≠Fr, r ∈ ℕ, the existence and uniqueness of the solution of a perfect, incompressible, irrotational free surface flow over a flat bottom, under the influence of gravity; as well as the corresponding hydraulic jump.
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