Traveling Quasi-periodic Water Waves with Constant Vorticity
Massimiliano Berti, Luca Franzoi, Alberto Maspero
Abstract
Abstract We prove the first bifurcation result of time quasi-periodic traveling wave solutions for space periodic water waves with vorticity. In particular, we prove the existence of small amplitude time quasi-periodic solutions of the gravity-capillary water waves equations with constant vorticity , for a bidimensional fluid over a flat bottom delimited by a space-periodic free interface. These quasi-periodic solutions exist for all the values of depth, gravity and vorticity, and restrict the surface tension to a Borel set of asymptotically full Lebesgue measure.
Topics & Concepts
VorticityLebesgue measureMathematical analysisPotential vorticityCapillary waveMathematicsConstant (computer programming)Gravity waveSurface tensionAmplitudePhysicsClassical mechanicsLebesgue integrationGravitational waveMechanicsVortexOpticsQuantum mechanicsComputer scienceProgramming languageOcean Waves and Remote SensingCoastal and Marine DynamicsArctic and Antarctic ice dynamics