  Galactic cosmic ray transport relies on the existence of turbulence on scales
comparable with the gyration radius of the particles and with wavenumber vector
oriented along the local magnetic field. In the standard picture, in which
turbulence is injected at large scales and cascades down to smaller scales, it
is all but guaranteed that the turbulent fluctuations at the scales relevant
for resonant scattering may be present, either because of anisotropic cascading
or because of the onset of damping processes. This raises questions on the
nature of cosmic-ray scattering, especially at energies $\gtrsim 1$ TeV, where
self-generation is hardly relevant. Here, by means of numerical simulations of
charged test-particles in a prescribed magnetic field, we perform a
gedankenexperiment aimed at investigating particle diffusion in a situation in
which turbulence is mainly present at large scales, and discuss possible
implications of this setup for cosmic-ray transport phenomenology.
