Smooth small solutions to gravity water waves with constant vorticity show arbitrary growth in high Sobolev norms, proving energy transfer to high frequencies and weak turbulence while the flow remains smooth.
Giuliani F.Quasi-periodic traveling waves on an infinitely deep fluid under gravity
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Transfer of energy for pure-gravity water waves with constant vorticity
Smooth small solutions to gravity water waves with constant vorticity show arbitrary growth in high Sobolev norms, proving energy transfer to high frequencies and weak turbulence while the flow remains smooth.