On the estimation of wave heights for periodic water waves from velocity and pressure data

Abstract

In this paper, we present some wave height estimates for the two-dimensional steady periodic water waves subject to the effect of vorticity. The lower bounds of wave heights for the case of positive vorticity and negative vorticity are derived, respectively. These results are associated with the pressure data at the flat bed and velocity data on trough line, and to the pressure data at the flat bed and velocity data on crest line, respectively. Furthermore, we provide some upper bounds of wave heights, which rely on velocity and pressure data at an arbitrary intermediate depth. In addition, we show some applications of the present model.