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The analysis shows exponential decay in gravity waves' velocity, indicating new bounds for free surface slopes.
We consider two-dimensional irrotational steady gravity waves and derive new explicit analytical bounds for the velocity field and the slope of the free surface. Using an auxiliary function tailored to the streamfunction formulation, we obtain an explicit exponential decay estimate which is optimal for linear waves. The same method yields a new slope estimate that improves existing bounds in the moderate-amplitude regime.
Evgeniy Lokharu (2026) studied this question.
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