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We present the analysis of a Chandra observation of the galaxy cluster Abell133, which has a cooling flow core, a central radio source, and a diffuse,filamentary radio source which has been classified as a radio relic.  The X-ray image shows that the core has a complex structure. The mostprominent feature is a "tongue" of emission which extends from the central cDgalaxy to the northwest and partly overlaps the radio relic. One possibility isthat this tongue is produced by Kelvin-Helmholtz (KH) instabilities through theinteraction between the cold gas around the cD galaxy and hot intraclustermedium. We estimate the critical velocity and time scale for the KH instabilityto be effective for the cold core around the cD galaxy. We find that the KHinstability can disrupt the cold core if the relative velocity is >~400 kms^-1. We compare the results with those of clusters in which sharp, undisruptedcold fronts have been observed; in these clusters, the low temperature gas intheir central regions has a more regular distribution. In contrast to Abell133, these cluster cores have longer timescales for the disruption of the coreby the KH instability when they are normalized to the timescale of the cDgalaxy motion. Thus, the other cores are less vulnerable to KH instability.Another possible origin of the tongue is that it is gas which has been upliftedby a buoyant bubble of nonthermal plasma that we identify with the observedradio relic. From the position of the bubble and the radio estimate of the ageof the relic source, we estimate avelocity of ~700 km s^-1 for the bubble. Thestructure of the bubble and this velocity are consistent with numerical modelsfor such buoyant bubbles. (abridged)Comment: 38 pages, 15 figures, accepted for publication in Ap

ChandraObservations of the Disruption of the Cool Core in A133