Control of water waves
Thomas Alazard, Pietro Baldi, Daniel Han-Kwan
TL;DR
This paper demonstrates that it is possible to precisely control small amplitude water waves in a short time by manipulating a localized part of the free surface, using the two-dimensional incompressible Euler equations with surface tension.
Contribution
It establishes local exact controllability of 2D water waves with surface tension, a novel result in the control of free surface fluid dynamics.
Findings
Exact controllability in short time for water waves with surface tension
Ability to generate arbitrary small amplitude gravity-capillary waves
Control achieved by localized surface manipulation
Abstract
We prove local exact controllability in arbitrary short time of the two-dimensional incompressible Euler equation with free surface, in the case with surface tension. This proves that one can generate arbitrary small amplitude periodic gravity-capillary water waves by blowing on a localized portion of the free surface of a liquid.
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