Abstract
David McLaughlin
Courant Institute
SPECTRAL BIFURCATIONS IN DISPERSIVE WAVE TURBULENCE
Dispersive wave turbulence is studied numerically for a class of
one-dimensional nonlinear wave equations. Both deterministic and random
white noise in time forcings are studied. Four distinct stable spectra
are observed -- the direct and inverse cascades of weak turbulence
(WT) theory, thermal equilibrium, and a fourth spectrum (MMT: Majda,
McLaughlin, Tabak). Each spectrum can describe long-time behavior, and
each can be only metastable (with quite diverse lifetimes) -- depending on
details of nonlinearity, forcing and dissipation. Cases of a long-lived
MMT transient state decaying to a state with WT spectra, and vice-versa,
are displayed. In the case of freely decaying turbulence, without
forcing, both cascades of weak turbulence are observed. These WT states
constitute the clearest and most striking numerical observations of WT
spectra to date -- over four decades of energy, and three decades of
spatial scales. Energy growth in time will be used to monitor numerically
the selection of MMT or WT spectra.
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