Linear water waves with vorticity: Rotational features and particle paths

Large-Amplitude Solitary Water Waves with Vorticity

We provide the first construction of exact solitary waves of large amplitude with an arbitrary distribution of vorticity. We use continuation to construct a global connected set of symmetric solitary waves of elevation, whose profiles decrease monotonically on either side of a central crest. This generalizes the classical result of Amick and Toland.

Symmetry of Solitary Water Waves with Vorticity

Symmetry and monotonicity properties of solitary water-waves of positive elevation with supercritical values of parameter are established for an arbitrary vorticity. The proof uses the detailed knowledge of asymptotic decay of supercritical solitary waves at infinity and the method of moving planes.

Exact Solitary Water Waves with Vorticity

The solitary water wave problem is to find steady free surface waves which approach a constant level of depth in the far field. The main result is the existence of a family of exact solitarywaves of small amplitude for an arbitrary vorticity. Each solution has a supercritical parameter value and decays exponentially at infinity. The proof is based on a generalized implicit function theorem of t...

Experimental study of the particle paths in solitary water waves.

We provide experiments that had been conducted to investigate the particle trajectory beneath a solitary water wave. Experimental results show that the surface drift is larger than the bottom drift. Meanwhile, the ratio of the net horizontal displacement to the total height of the trajectory at the free surface and subsurface will decrease with the initial vertical position and increase with th...

low-vorticity waves in deep water