  We present experimental observations suggesting that the non-diffusive
avalanche-like events are a prevalent and universal process of the electron
turbulent heat transport in tokamak core plasmas. They are observed in the low
confinement mode and the weak internal transport barrier tokamak plasmas in the
absence of magnetohydrodynamic instabilities. In addition, the electron
temperature profile corrugation, which indicates the existence of the $E \times
B$ shear flow layers, is clearly demonstrated as well as their dynamical
interaction with the avalanche-like events. The measured width of the profile
corrugation is around $45\rho_i$, which implies the mesoscale nature of the
structure.
