38 research outputs found
Weakly nonlinear non-symmetric gravity waves on water of finite depth
A weakly nonlinear Hamiltonian model for two-dimensional irrotational waves on water of finite depth is developed. The truncated model is used to study families of periodic travelling waves of permanent form. It is shown that non-symmetric periodic waves exist, which appear via spontaneous symmetry-breaking bifurcations from symmetric waves
Steep sharp-crested gravity waves on deep water
A new type of steady steep two-dimensional irrotational symmetric periodic
gravity waves on inviscid incompressible fluid of infinite depth is revealed.
We demonstrate that these waves have sharper crests in comparison with the
Stokes waves of the same wavelength and steepness. The speed of a fluid
particle at the crest of new waves is greater than their phase speed.Comment: 4 pages, 2 figures, submitted to Phys. Rev. Let
The adjoining cell mapping and its recursive unraveling, Part II: Application to selected problems
Several applications of the adjoining cell mapping technique are provided here by employing the adaptive mapping unraveling algorithm to analyze smooth and pathological autonomous dynamical systems. The performance of an implementation of recursive unraveling algorithm is also illustrated regarding its low memory requirements for computa- tional purposes when compared with the simple cell mapping method. The applications considered here illustrate the effectiveness of the adjoining cell mapping technique in its ability to determine limit cycles and to unravel nonstandard dynamics. The advantages of this new technique of global analysis over the simple cell mapping method are discussed