We present the results of a very deep ( 500 ks ) Chandra observation , along with tailored numerical simulations , of the nearest , best resolved cluster cold front in the sky , which lies 90 kpc ( 19 ^ { \prime } ) to the northwest of M 87 . The northern part of the front appears the sharpest , with a width smaller than 2.5 kpc ( 1.5 Coulomb mean free paths ; at 99 per cent confidence ) . Everywhere along the front , the temperature discontinuity is narrower than 4–8 kpc and the metallicity gradient is narrower than 6 kpc , indicating that diffusion , conduction and mixing are suppressed across the interface . Such transport processes can be naturally suppressed by magnetic fields aligned with the cold front . Interestingly , comparison to magnetohydrodynamic simulations indicates that in order to maintain the observed sharp density and temperature discontinuities , conduction must also be suppressed along the magnetic field lines . However , the northwestern part of the cold front is observed to have a nonzero width . While other explanations are possible , the broadening is consistent with the presence of Kelvin-Helmholtz instabilities ( KHI ) on length scales of a few kpc . Based on comparison with simulations , the presence of KHI would imply that the effective viscosity of the intra-cluster medium is suppressed by more than an order of magnitude with respect to the isotropic Spitzer-like temperature dependent viscosity . Underneath the cold front , we observe quasi-linear features that are \sim 10 per cent brighter than the surrounding gas and are separated by \sim 15 kpc from each other in projection . Comparison to tailored numerical simulations suggests that the observed phenomena may be due to the amplification of magnetic fields by gas sloshing in wide layers below the cold front , where the magnetic pressure reaches \sim 5 –10 per cent of the thermal pressure , reducing the gas density between the bright features .