On Optimal Canonical Variables in the Theory of Ideal Fluid with Free Surface

Abstract

Dynamics of ideal fluid with free surface can be effectively solved by perturbing the Hamiltonian in weak nonlinearity limit. However it is shown that perturbation theory, which includes third and fourth order terms in the Hamiltonian, results in the ill-posed equations because of short wavelength instability. To fix that problem we introduce the canonical Hamiltonian transform from original physical variables to new variables for which instability is absent.

arXiv comment23 page, 6 figures, submitted to Physica D

References in corpus (4)

• Freely decaying weak turbulence for sea surface gravity waves
• Weak Turbulent Kolmogorov Spectrum for Surface Gravity Waves
• Weak turbulence of gravity waves
• Decay of the monochromatic capillary wave

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