  We investigate various aspects of a geometric flow defined using the Bach
tensor. Firstly, using a well-known split of the Bach tensor components for
$(2,2)$ unwarped product manifolds, we solve the Bach flow equations for
typical examples of product manifolds like $S^2\times S^2$, $R^2\times S^2$. In
addition, we obtain the fixed point condition for general $(2,2)$ manifolds and
solve it for a restricted case. Next, we consider warped manifolds. For Bach
flows on a special class of asymmetrically warped four manifolds, we reduce the
flow equations to a first order dynamical system, which is solved exactly to
find the flow characteristics. We compare our results for Bach flow with those
for Ricci flow and discuss the differences qualitatively. Finally, we conclude
by mentioning possible directions for future work.
