A function $\eta$ is a wave shape if it, along with its streamfunction, satisfies Bernoulli's condition. Thus far only constant, or flat water, shapes are guaranteed to exist. Intuition suggests that there should be non-constant shapes. Here we provide and investigate a variational interpretation of this problem. We numerically study the water wave problem at various vorticities and pressure values. The approach proves well-suited for the implementation of numerical Mountain Pass techniques developed by Choi and McKenna and, using such techniques, we locate numerous non-constant solutions.
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