Neutrino experiments have always been comparatively low rate devices
compared to collider-based projects.  However, this is changing.  The
currently operational US long baseline neutrino oscillation experiment
NOvA has 14kt of liquid scintillator on the surface.  That results in
upwards of 100kHz of cosmic rays, generating more than a GB/s of raw
data.  Only a small fraction of that data needs to be stored, so a
software-based trigger system has been developed.  DUNE, the next
generation long baseline experiment, will be underground in SURF: but it
is a large liquid argon TPC, so will generate more than a TB/s of
waveforms per 10kT module.  Plans for how to save the most useful 
30 PB/year of that data involve a similar overall scheme as NOvA: but at 
a very different scale.