  Gamma-ray emission from the Crab Nebula has been recently shown to be
unsteady. In this paper, we study the flux and spectral variability of the Crab
above 100 MeV on different timescales ranging from days to weeks. In addition
to the four main intense and day-long flares detected by AGILE and Fermi-LAT
between Sept. 2007 and Sept. 2012, we find evidence for week-long and less
intense episodes of enhanced gamma-ray emission that we call "waves".
Statistically significant "waves" show timescales of 1-2 weeks, and can occur
by themselves or in association with shorter flares. We present a refined flux
and spectral analysis of the Sept. - Oct. 2007 gamma-ray enhancement episode
detected by AGILE that shows both "wave" and flaring behavior. We extend our
analysis to the publicly available Fermi-LAT dataset and show that several
additional "wave" episodes can be identified. We discuss the spectral
properties of the September 2007 "wave"/flare event and show that the physical
properties of the "waves" are intermediate between steady and flaring states.
Plasma instabilities inducing "waves" appear to involve spatial distances l
\sim 10^{16} cm and enhanced magnetic fields B \sim (0.5 - 1) mG. Day-long
flares are characterized by smaller distances and larger local magnetic fields.
Typically, the deduced total energy associated with the "wave" phenomenon (E_w
\sim 10^{42} erg, where E_w is the kinetic energy of the emitting particles) is
comparable with that associated to the flares, and can reach a few percent of
the total available pulsar spindown energy. Most likely, flares and waves are
the product of the same class of plasma instabilities that we show acting on
different timescales and radiation intensities.
