Geometric phases of water waves

Abstract

Recently, Banner et al. (2014) highlighted a new fundamental property of open ocean wave groups, the so-called crest slowdown. For linear narrowband waves, this is related to the geometric and dynamical phase velocities $U_d$ and $U_g$ associated with the parallel transport through the principal fiber bundle of the wave motion with $U(1)$ symmetry. The theoretical predictions are shown to be in fair agreement with ocean field observations, from which the average crest speed $c=U_d+U_g$ with $c/U_d\approx 0.8$ and $U_g/U_d\approx -0.2$.

References in corpus (2)

• Linking reduced breaking crest speeds to unsteady nonlinear water wave group behavior
• On certain properties of the compact Zakharov equation

Cited by in corpus (5)

• Kinematics of fluid particles on the sea surface. Hamiltonian theory
• Symmetry reduction of turbulent pipe flows
• Hopf fibrations for turbulent pipe flows
• Crest speeds of unsteady surface water waves
• Berry Phases in the Reconstructed KdV Equation