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Ocean submesoscale features appear to be widespread in the surface mixed layer and thus may be an important link in the energy pathway from large to small scales. An example is the "spiral eddy," for which several theories have been proposed. High-resolution radar imagery should be useful in testing these theories, but there have as yet been no simulations of radar imagery from first principles. As a step in this direction, we developed a capability to simulate imagery using a full-spectral calculation that includes the effects of both wave-current interaction and wave damping due to a surface film. A particular model of a spiral eddy is used to specify the surface velocity field and film distribution. Imagery is then simulated for a range of radar frequencies, wind speeds, initial film pressures, and relative radar view directions. For winds of 3-8 m/s and an initial film pressure of 0.5 mN/m, imagery for shorter radar wavelengths (X- and C-band) is dominated by the effects of film damping. For longer wavelengths (L- and P-band) wave-current interactions and film damping are of comparable magnitude; but for higher initial film pressures, the L- and P-band images also become dominated by film damping. L-band imagery, in particular, is highly sensitive to the initial value of film pressure, and such a result may have implications for determining properties of seawater films. Overall, the radar simulations produce surface patterns having characteristics that resemble radar imagery of real ocean spiral eddies.