  We perform a unique direct numerical simulation of Euler turbulence using
delta-correlated velocity field as an initial condition, and report a full
range of $k^2$ and $k$ energy spectra for 3D and 2D flows respectively, zero
energy flux, and Maxwell-Boltzmann distribution for the velocity field. These
are direct verification of the predictions of the absolute equilibrium theory
of turbulence. For a coherent vortex as an initial condition, Euler turbulence
transitions from a mixture of nonequilibrium-equilibrium state to a equilibrium
state through a process called thermalization. In this letter, we present a
model for thermalization in Euler turbulence.
