  X-ray images of galaxy clusters and gas-rich elliptical galaxies show a
wealth of small-scale features which reflect fluctuations in density and/or
temperature of the intra-cluster medium. In this paper we study these
fluctuations in M87/Virgo, to establish whether sound waves/shocks, bubbles or
uplifted cold gas dominate the structure. We exploit the strong dependence of
the emissivity on density and temperature in different energy bands to
distinguish between these processes. Using simulations we demonstrate that our
analysis recovers the leading type of fluctuation even in the presence of
projection effects and temperature gradients. We confirm the isobaric nature of
cool filaments of gas entrained by buoyantly rising bubbles, extending to 7' to
the east and south-west, and the adiabatic nature of the weak shocks at 40" and
3' from the center. For features of 5--10 kpc, we show that the central 4'x 4'
region is dominated by cool structures in pressure equilibrium with the ambient
hotter gas while up to 30 percent of the variance in this region can be
ascribed to adiabatic fluctuations. The remaining part of the central 14'x14'
region, excluding the arms and shocks described above, is dominated by
apparently isothermal fluctuations (bubbles) with a possible admixture (at the
level of about 30 percent) of adiabatic (sound waves) and by isobaric
structures. Larger features, of about 30 kpc, show a stronger contribution from
isobaric fluctuations. The results broadly agree with an AGN feedback model
mediated by bubbles of relativistic plasma.
