  We prove a general result about the short time existence and uniqueness of
second order geometric flows transverse to a Riemannian foliation on a compact
manifold. Our result includes some flows already existing in literature, as the
transverse Ricci flow, the Sasaki-Ricci flow and the Sasaki J-flow and
motivates the study of other evolution equations. We also introduce a
transverse version of the Kaehler-Ricci flow adapting some classical results to
the foliated case.
