The kinematic complexity and the favorable position of M51 on the sky make this galaxy an ideal target to test different theories of spiral arm dynamics. Taking advantage of the new high resolution PdBI Arcsecond Whirlpool Survey (PAWS) data, we undertake a detailed kinematic study of M51 to characterize and quantify the origin and nature of the non-circular motions. Using a tilted-ring analysis supported by several other archival datasets we update the estimation of M51s position angle (PA=(173 +/- 3) deg) and inclination (i=(22 +/- 5) deg). Harmonic decomposition of the high resolution (40 pc) CO velocity field shows the first kinematic evidence of an m=3 wave in the inner disk of M51 with a corotation at R(CR,m=3)=1.1 +/- 0.1 kpc and a pattern speed of Omega_p(m=3) = 140 km/(s kpc). This mode seems to be excited by the nuclear bar, while the beat frequencies generated by the coupling between the m=3 mode and the main spiral structure confirm its density-wave nature. We observe also a signature of an m=1 mode that is likely responsible for the lopsidedness of M51 at small and large radii. We provide a simple method to estimate the radial variation of the amplitude of the spiral perturbation (Vsp) attributed to the different modes. The main spiral arm structure has <Vsp>=50-70 km/s, while the streaming velocity associated with the m=1 and m=3 modes is, in general, 2 times lower. Our joint analysis of HI and CO velocity fields at low and high spatial resolution reveals that the atomic and molecular gas phases respond differently to the spiral perturbation due to their different vertical distribution and emission morphology.
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