The FermiPastaUlam recurrence and related phenomena for 1 D shallowwater waves in a finite basin
Abstract
Different regimes of the FermiPastaUlam (FPU) recurrence are simulated numerically for fully nonlinear "onedimensional" potential water waves in a finitedepth flume between two vertical walls. In such systems, the FPU recurrence is closely related to the dynamics of coherent structures approximately corresponding to solitons of the integrable Boussinesq system. A simplest periodic solution of the Boussinesq model, describing a single soliton between the walls, is presented in analytic form in terms of the elliptic Jacobi functions. In the numerical experiments, it is observed that depending on the number of solitons in the flume and their parameters, the FPU recurrence can occur in a simple or complicated manner, or be practically absent. For comparison, the nonlinear dynamics of potential water waves over nonuniform beds is simulated, with initial states taken in the form of several pairs of colliding solitons. With a mildslope bed profile, a typical phenomenon in the course of evolution is the appearance of relatively high (rogue) waves, while for random, relatively shortcorrelated bed profiles it is either the appearance of tall waves or the formation of sharp crests at moderateheight waves.
 Publication:

Soviet Journal of Experimental and Theoretical Physics
 Pub Date:
 February 2012
 DOI:
 10.1134/S1063776111160084
 arXiv:
 arXiv:1104.0853
 Bibcode:
 2012JETP..114..343R
 Keywords:

 Physics  Fluid Dynamics
 EPrint:
 revtex4, 10 pages, 33 figures