  It has been observed that the direction in which a sand dune extends its
crest line depends on seasonal variation of wind direction; when the variation
is small, the crest line develops more or less perpendicularly to the mean wind
direction to form a transverse dune with some undulation. In the case of
bimodal wind with a large relative angle, however, the dune extends its crest
along the mean wind direction and evolves into an almost straight longitudinal
dune. Motivated by these observations, we investigate the dynamical stability
of isolated dunes using the crest line model, where the dune dynamics is
represented by its crest line motion. First, we extend the previous linear
stability analysis under the unidirectional wind to the case with non-zero
slant angle between the wind direction and the normal direction of the crest
line, and show that the stability diagram does not depend on the slant angle.
Secondly, we examine how the linear stability is affected by the seasonal
changes of wind direction in the case of bimodal wind with equal strength and
duration. For the transverse dune, we find that the stability is virtually the
same with that for the unidirectional wind as long as the dune evolution during
a season is small. On the other hand, in the case of the longitudinal dune, the
dispersions of the growth rates for the perturbation are drastically different
from those of the unidirectional wind, and we find that the largest growth rate
is always located at $k = 0$. This is because the growth of the perturbation
with $k \ne 0$ is canceled by the alternating wind from opposite sides of the
crest line even though it grows during each duration period of the bimodal
wind.
