We found that loosely wound spiral shocks in an isothermal gas disk caused by a non-axisymmetric potential are hydrodynamically unstable, if the shocks are strong enough. High resolution, global hydrodynamical simulations using three different numerical schemes, i.e. AUSM, CIP, and SPH, show similarly that trailing spiral shocks with the pitch angle of larger than ~10 deg wiggle, and clumps are developed in the shock-compressed layer. The numerical simulations also show clear wave crests that are associated with ripples of the spiral shocks. The spiral shocks tend to be more unstable in a rigidly rotating disk than in a flat rotation. This instability could be an origin of the secondary structures of spiral arms, i.e. the spurs/fins, observed in spiral galaxies. In spite of this local instability, the global spiral morphology of the gas is maintained over many rotational periods. The Kelvin-Helmholtz (K-H) instability in a shear layer behind the shock is a possible mechanism for the wiggle instability. The Richardson criterion for the K-H stability is expressed as a function of the Mach number, the pitch angle, and strength of the background spiral potential. The criterion suggests that spiral shocks with smaller pitch angles and smaller Mach numbers would be more stable, and this is consistent with the numerical results.
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