  The long-time solutions of the Galerkin-truncated three-dimensional,
incompressible Euler equation relax to an absolute equilibrium as a consequence
of phase space and kinetic energy conservation in such a finite-dimensional
system. These thermalized solutions are characterised by a Gibbs distribution
of the velocity field and kinetic energy equipartition amongst its (finite)
Fourier modes. We now show, through detailed numerical simulations, the
triggers for the inevitable thermalization in physical space and how the
problem is reducible to an effective one-dimensional problem making comparisons
with the more studied Burgers equation feasible. We also discuss how our
understanding of the mechanism of thermalization can be exploited to
numerically obtain dissipative solutions of the Euler equations and evidence
for or against finite-time blow-up in computer simulations.
