Numerical simulations of the buoyant phase of a radio-galaxies evolution show that appreciable amounts of ICM from the cluster core can become entrained in the ``wake'' of a buoyantly rising plume of radio plasma (Brüggen et al. 2002; Reynolds, Heinz, & Begelman 2002). This material adiabatically decompresses and cools as it is dragged upwards in the cluster potential, and would appear as distinct filaments of cold and dense material strung out along the path of the buoyant plume.
As discussed by Young, Wilson & Mundell (2002), these wakes of cold
gas are probably responsible for the arc-like feature seen in ROSAT-HRI and Chandra-ACIS observations of M87 and the core
of the Virgo cluster. This structure is composed of narrow filaments
or columns of cold gas (with 
, compared with 
for the surrounding ICM), probably in pressure equilibrium with
their surroundings, that extend for 2-3arcmins East and South-West
of M87. They are coincident with, but more more narrowly confined
than, the 90cm radio arc observed by Owen, Eilek & Kassim (2000).
This supports the idea that the filament has been entrained and pulled
out of the central parts of M87/Virgo by a buoyantly rising plume.
However, it seems unlikely that such a model can explain the SW ridge of A 4059. There is no indication of any radio-lobe (even a very old one) in the SW direction, i.e., there is no radio emission and no ICM cavity in that quadrant of the cluster. Furthermore, the SW ridge does not take on the form of a narrow filament reaching out from the cD galaxy, as would be expected for wake material on the basis of both the numerical simulations and the Young et al. (2002) observations of Virgo. Instead, the SW ridge is a rather broad and flaring feature extending from the cD galaxy. On the basis of these two observations, we reject the hypothesis that the SW ridge corresponds to cool material that has been entrained in the wake of a buoyantly rising plume of radio-plasma.