The nonlinear asymptotic theory of bar-driven spiral density waves developed by Yuan & Kuo is applied to the spiral structure in the gas-dominated central disk of NGC 1068 and M100. Comparison with radio interferometric observations confirms the predictions that a pair of tightly wound spirals in the central region can be regarded as the signature of a rapidly rotating bar (in the case of NGC 1068) and that a pair of relatively open spirals as the signature of a slowly rotating bar (in the case of M100). Furthermore, consistent with the theory, we find that streaming motions along the spiral arms are radially outward for the tightly wound spiral arms and radially inward for the relatively open spirals. Associated with the spiral density waves is the angular momentum transport between the bar and the disk, which eventually results in redistribution of the gas in the disk in slow long-term inflows or outflows. We discuss the implications of such flows in, for example, fueling AGNs or in starburst ring activities.