We consider the mildly nonlinear response of a fluid disk with pressure, viscosity, and self-gravity to spiral stellar forcing, as a model of the interstellar medium in spiral galaxies. We analyze nonlinear effects through a quasilinear flow analysis ordered by successive powers of a dimensionless spiral perturbing force F, which is the ratio of imposed nonaxisymmetric gravitational to axisymmetric gravitational forces. Ultraharmonic resonances of order n arise where mn(OMEGA(p) - OMEGA) = +/- kappa for spiral pattern speed OMEGA(p) in a galaxy with m spiral arms in the stellar disk. Waves with mn arms are launched from a position (typically slightly displaced from the resonance) where the wavenumber of a free wave matches n times the wavenumber of the spiral forcing. The n = 1 case corresponds to the usual Lindblad resonances; the n = 2 case corresponds to the lowest order ultraharmonic resonances found at the 4:1 commensurability (of the material frequency relative to the pattern with the epicyclic frequency) inside corotation and the 1:4 resonance outside corotation. The launched short wave in the gas is an interarm feature that is more tightly wrapped than the stellar wave. The gas wave extracts energy and angular momentum from the stellar wave, causing it to damp. The torque generated by ultraharmonic resonance of order n is equal to T2n = +/- mn-sigma-0D(n)-1F2n(k2r(n)2 + m2)n-1-OMEGA-4r(n)4h(n), where sigma-0 is the gas surface density at resonance, D(n) = dD(n)/d log r(r = r(n)) for D(n) = kappa-2 - n2m2 (OMEGA - OMEGA(p))2, resonant radius r(n) is defined such that D(n)(r(n)) = 0, OMEGA-r(n) is the rotation velocity at resonance, and h(n) is a positive, dimensionless function of stellar spiral galactic parameters. The torque is negative inside corotation and positive outside. For sufficiently thin disks, it is independent of the gas sound speed, viscosity, and self-gravity for each k, m, and n. The resulting stellar wave damping time due to the gas wave at the n = 2 gas resonance is of order 10(9) yr for parameters appropriate to M81. The application of our results to the stellar disk alone reveals even stronger damping, as stars undergo Landau damping of the short wave. For parameters in M81, damping times are less than 10(9) yr (although saturation effects may limit the damping rate). If this mechanism limits spiral wave growth and the wave excitation process relies upon the corotation resonance, then we expect that spiral structure is not truncated at the 4:1 ultraharmonic resonance, and may even produce stronger amplitudes near corotation that lies outside the 4:1 resonance.
