The Fermi-Pasta-Ulam recurrence and related phenomena for 1D shallow-water waves in a finite basin

Journal Article · Wed Feb 15 00:00:00 EST 2012 · Journal of Experimental and Theoretical Physics

DOI:https://doi.org/10.1134/S1063776111160084· OSTI ID:22027912

Ruban, V. P., E-mail: [e-mail] ^[1]

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1. Russian Academy of Sciences, Landau Institute for Theoretical Physics (Russian Federation)

Different regimes of the Fermi-Pasta-Ulam (FPU) recurrence are simulated numerically for fully nonlinear 'one-dimensional' potential water waves in a finite-depth 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 mild-slope bed profile, a typical phenomenon in the course of evolution is the appearance of relatively high (rogue) waves, while for random, relatively short-correlated bed profiles it is either the appearance of tall waves or the formation of sharp crests at moderate-height waves.

• OSTI ID: 22027912
• Journal Information: Journal of Experimental and Theoretical Physics, Vol. 114, Issue 2; Other Information: Copyright (c) 2012 Pleiades Publishing, Ltd.; Country of input: International Atomic Energy Agency (IAEA); ISSN 1063-7761
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
COMPARATIVE EVALUATIONS
COMPUTERIZED SIMULATION
EVOLUTION
INTEGRAL CALCULUS
JACOBIAN FUNCTION
MATHEMATICAL SOLUTIONS
NONLINEAR PROBLEMS
ONE-DIMENSIONAL CALCULATIONS
PERIODICITY
POTENTIALS
RANDOMNESS
SOLITONS
WATER WAVES