  Solutions to finite-dimensional (all spatial Fourier modes set to zero beyond
a finite wavenumber $K_G$), inviscid equations of hydrodynamics at long times
are known to be at variance with those obtained for the original infinite
dimensional partial differential equations or their viscous counterparts.
Surprisingly, the solutions to such Galerkin-truncated equations develop sharp
localised structures, called {\it tygers} [Ray, et al., Phys. Rev. E {\bf 84},
016301 (2011)], which eventually lead to completely thermalised states
associated with an equipartition energy spectrum. We now obtain, by using the
analytically tractable Burgers equation, precise estimates, theoretically and
via direct numerical simulations, of the time $\tau_c$ at which thermalisation
is triggered and show that $\tau_c \sim \kg^\xi$, with $\xi = -4/9$. Our
results have several implications including for the analyticity strip method to
numerically obtain evidence for or against blow-ups of the three-dimensional
incompressible Euler equations.
