LAUSR

We show that in a three-dimensional gravity water flow with a constant non-vanishing vorticity vector (Ω1, Ω2, Ω3), the free surface, the pressure, and the velocity field present no variations in the direction orthogonal to the direction of motion. In addition, the second component of the velocity field is constant throughout the flow. Moreover, we prove that the vertical component, Ω3, of the vorticity vector has to vanish. This latter fact turns out to be of crucial importance in proving the absence of variations of the flow in the direction that is orthogonal to the direction of the surface wave propagation. Our results are obtained under general assumptions: both the free surface and the flow beneath are allowed to be time dependent in the most general way.We show that in a three-dimensional gravity water flow with a constant non-vanishing vorticity vector (Ω1, Ω2, Ω3), the free surface, the pressure, and the velocity field present no variations in the direction orthogonal to the direction of motion. In addition, the second component of the velocity field is constant throughout the flow. Moreover, we prove that the vertical component, Ω3, of the vorticity vector has to vanish. This latter fact turns out to be of crucial importance in proving the absence of variations of the flow in the direction that is orthogonal to the direction of the surface wave propagation. Our results are obtained under general assumptions: both the free surface and the flow beneath are allowed to be time dependent in the most general way.