  We study a planar random motion $\big(X(t),Y(t)\big)$ with orthogonal
directions which can turn clockwise, counterclockwise and reverse its direction
each with a different probability. The support of the process is given by a
time-varying square and the singular distributions on the boundary and the
diagonals of the square are obtained. In the interior of the support, we study
the hydrodynamic limit of the distribution. We then investigate the time $T(t)$
spent by the process moving vertically and the joint distribution of
$\big(T(t),Y(t)\big)$. We prove that, in the hydrodynamic limit, the process
$\big(X(t),Y(t)\big)$ spends half the time moving vertically.
