We present high-quality VLA images of the FR I radio galaxy 3C 31 in the frequency range 1365 to 8440 MHz with angular resolutions from 0.25 to 40 arcsec. Our new images reveal complex, well resolved filamentary substructure in the radio jets and tails. We also use these images to explore the spectral structure of 3C 31 on large and small scales. We infer the apparent magnetic field structure by correcting for Faraday rotation. Some of the intensity substructure in the jets is clearly related to structure in their apparent magnetic field: there are arcs of emission where the degree of linear polarization increases, with the apparent magnetic field parallel to the ridges of the arcs. The spectral indices are significantly steeper (0.62) within 7 arcsec of the nucleus than between 7 and 50 arcsec (0.52 - 0.57). The spectra of the jet edges are also slightly flatter than the average for their surroundings. At larger distances, the jets are clearly delimited from surrounding larger-scale emission both by their flatter radio spectra and by sharp brightness gradients. The spectral index of 0.62 in the first 7 arcsec of 3C 31s jets is very close to that found in other FR I galaxies where their jets first brighten in the radio and where X-ray synchrotron emission is most prominent. Farther from the nucleus, where the spectra flatten, X-ray emission is fainter relative to the radio. The brightest X-ray emission from FR I jets is therefore not associated with the flattest radio spectra, but with a particle-acceleration process whose characteristic energy index is 2.24. The spectral flattening with distance from the nucleus occurs where our relativistic jet models require deceleration, and the flatter-spectra at the jet edges may be associated with transverse velocity shear. (Slightly abridged)
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