disk galaxy without external perturbations and a bar structure [^1]. @SellwoodCarlberg1984 claimed that self-induced stellar spiral structures in stellar disks are not stationary and fade away within an interval of about ten rotational periods. Their study stresses on the significance of cooling mechanisms, such as dissipation by the interstellar medium (ISM), that are required to maintain stellar spiral arms. More recently, @Fujii+2011 used 3-D $N$-body simulations to show that although stellar spiral arms are short-lived, they are also recurrently formed, and as a result, the spiral features are maintained over 10 Gyr [see also @Sellwood2011]. This is because of negative feedback that causes the dynamical heating of stars in the disk galaxies due to spirals. The non-steady spirals are also subject to a similar phenomenon when the dynamics of the ISM are self-consistently solved with stars in disk galaxies. Both the stellar spirals and the ISM undergo motion in the wake of the the galactic rotation [see also @Grand+2012]. In fact, the spirals can be considered as being “wound”. The ISM forms dense regions associated with the non-steady stellar spirals; however, these regions are not the conventional “galactic shocks”[@Wada+2011].

The existence of non-steady stellar spirals has been suggested by certain 