Tangential discontinuities known as cold fronts ( CFs ) are abundant in groups and clusters of galaxies ( GCs ) . The relaxed , spiral-type CFs were initially thought to be isobaric , but a significant , 10 \% – 20 \% jump in the thermal pressure P _ { t } was reported when deprojected CFs were stacked , interpreted as missing P _ { t } below the CFs ( i.e . at smaller radii r ) due to a locally-enhanced nonthermal pressure P _ { nt } . We report a significant ( \sim 4.3 \sigma ) deprojected jump in P _ { t } across a single sharp CF in the Centaurus cluster . Additional seven CFs are deprojected in the GCs A2029 , A2142 , A2204 , and Centaurus , all found to be consistent ( stacked : \sim 1.9 \sigma ) with similar pressure jumps . Combining our sample with high quality deprojected CFs from the literature indicates pressure jumps at significance levels ranging between 2.7 \sigma and 5.0 \sigma , depending on assumptions . Our nominal results are consistent with P _ { nt } \simeq ( 0.1 \mbox { - - } 0.3 ) P _ { t } just below the CF . We test different deprojection and analysis methods to confirm that our results are robust , and show that without careful deprojection , an opposite pressure trend may incorrectly be inferred . Analysing all available deprojected data , we also find : ( i ) a nearly constant CF contrast q of density and temperature within each GC , monotonically increasing with the GC mass M _ { 200 } as q \propto M _ { 200 } ^ { 0.23 \pm 0.04 } ; ( ii ) hydrostatic mass discontinuities indicating fast bulk tangential flows below all deprojected CFs , with a mean Mach number \sim 0.76 ; and ( iii ) the newly deprojected CFs are consistent ( stacked : \sim 2.9 \sigma ) with a 1.25 ^ { +0.09 } _ { -0.08 } metallicity drop across the CF . These findings suggest that GCs quite generally harbor extended spiral flows .