Pure gravity traveling quasi‐periodic water waves with constant vorticity
Massimiliano Berti, Luca Franzoi, Alberto Maspero
Abstract
Abstract We prove the existence of small amplitude time quasi‐periodic solutions of the pure gravity water waves equations with constant vorticity , for a bidimensional fluid over a flat bottom delimited by a space periodic free interface. Using a Nash‐Moser implicit function iterative scheme we construct traveling nonlinear waves which pass through each other slightly deforming and retaining forever a quasiperiodic structure. These solutions exist for any fixed value of depth and gravity and restricting the vorticity parameter to a Borel set of asymptotically full Lebesgue measure.
Topics & Concepts
MathematicsVorticityQuasiperiodic functionMathematical analysisGravity waveLebesgue measureConstant (computer programming)AmplitudePeriodic functionGravitational waveClassical mechanicsLebesgue integrationPhysicsMechanicsVortexAstrophysicsQuantum mechanicsProgramming languageComputer scienceOcean Waves and Remote SensingCoastal and Marine DynamicsOceanographic and Atmospheric Processes