  Generalizing results of Chou and Wang \cite{1} we study the flows of the
leaves $(M_{\Theta})_{\Theta>0}$ of a foliation of $\mathbb{R}^{n+1}\setminus
\{0\}$ consisting of uniformly convex hypersurfaces in the direction of their
outer normals with speeds $-\log(F/f)$. For quite general functions $F$ of the
principal curvatures of the flow hypersurfaces and $f$ a smooth and positive
function on $S^n$ (considered as a function of the normal) we show that there
is a distinct leaf $M_{\Theta_{*}}$ in this foliation with the property that
the flow starting from $M_{\Theta_{*}}$ converges to a translating solution of
the flow equation. Furthermore, when starting the flow from a leave inside
$M_{\Theta_{*}}$ it shrinks to a point and when starting the flow from a leave
outside $M_{\Theta_{*}}$ it expands to infinity. While \cite{1} considered this
mechanism with $F$ equal to the Gauss curvature we allow $F$ to be among others
the elementary symmetric polynomials $H_k$. We, furthermore, show that such
kind of behavior is robust with respect to relaxing certain assumptions at
least in the rotationally symmetric and homogeneous degree one curvature
function case.
