Radio and optical images of the M87 jet show bright filaments, twisted into an apparent double helix, extending from HST-1 to knot A. Proper motions within the jet suggest a decelerating jet flow passing through a slower, accelerating wave pattern. We use these observations to develop a mass and energy flux conserving model describing the jet flow and conditions along the jet. We determine the cocoon conditions required if the twisted filaments are the result of the Kelvin-Helmholtz (KH) unstable elliptical mode. We find that the cocoon must be cooler than the jet at HST-1 but must be about as hot as the jet at knot A. Under these conditions we find that the observed filament wavelength is near the elliptical mode maximum growth rate and growth is rapid enough for the filaments to develop and saturate well before HST-1. We generate a pseudo-synchrotron image of a model jet carrying a combination of normal modes of the KH instability. The pseudo-synchrotron image of the jet reveals: (1) that a slow decline in the model jets surface brightness is still about five times faster than the real jet; (2) that KH produced dual helically twisted filaments can appear qualitatively similar to those on the real jet if any helical perturbation to the jet is very small or nonexistent inside knot A; (3) that the knots in the real jet cannot be associated with the twisted filamentary features and are unlikely to be the result of a KH instability. The existence of the knots in the real jet, the limb brightening of the real jet in the radio, and the slower decline of the surface brightness of the real jet indicate that additional processes --- such as unsteady jet flow and internal particle acceleration --- are occurring within the jet. Disruption of the real jet beyond knot A by KH instability is consistent with the jet and cocoon conditions we find at knot A.
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