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We analysed the deep archival Chandra observations of the high-temperature galaxy cluster Abell 2319 to investigate the prominent cold front in its core. The main sharp arc of the front shows wiggles, or variations of the radius of the density jump along the arc. At the southern end of the arc is a feature that resembles a Kelvin-Helmholtz (KH) eddy, beyond which the sharp front dissolves. These features suggest that KH instabilities develop at the front. Under this assumption, we can place an upper limit on the ICM viscosity that is several times below the isotropic Spitzer value. Other features include a split of the cold front at its northern edge, which may be another KH eddy. There is a small pocket of hot, less-dense gas inside the cold front, which may indicate a `hole' in the front's magnetic insulation layer that lets the heat from the outer gas to penetrate inside the front. Finally, a large concave brightness feature southwest of the cluster core can be caused by the gasdynamic instabilities. We speculate that it can also be an inner boundary of a giant AGN bubble, similar to that in Ophiuchus. If the latter interpretation is supported by better radio data, this could be a remnant of another extremely powerful AGN outburst.