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Gamma-ray emission from the Crab Nebula has been recently shown to beunsteady. In this paper, we study the flux and spectral variability of the Crababove 100 MeV on different timescales ranging from days to weeks. In additionto the four main intense and day-long flares detected by AGILE and Fermi-LATbetween Sept. 2007 and Sept. 2012, we find evidence for week-long and lessintense episodes of enhanced gamma-ray emission that we call "waves".Statistically significant "waves" show timescales of 1-2 weeks, and can occurby themselves or in association with shorter flares. We present a refined fluxand spectral analysis of the Sept. - Oct. 2007 gamma-ray enhancement episodedetected by AGILE that shows both "wave" and flaring behavior. We extend ouranalysis to the publicly available Fermi-LAT dataset and show that severaladditional "wave" episodes can be identified. We discuss the spectralproperties of the September 2007 "wave"/flare event and show that the physicalproperties 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-longflares 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) iscomparable with that associated to the flares, and can reach a few percent ofthe total available pulsar spindown energy. Most likely, flares and waves arethe product of the same class of plasma instabilities that we show acting ondifferent timescales and radiation intensities.

Variable gamma-ray emission from the Crab Nebula: short flares and long "waves"