ABSTRACT Some red giant envelopes present spiral structures (seen either in dust-scattered stellar continuum or in molecular line emission), the most striking example probably being AFGL 3068. This object has been modeled (both analytically and numerically) in terms of a wind ejected from a star in orbit around a binary companion. We revisit both analytical models and 3D simulations of a wind from an orbiting red giant star, and extend the numerical simulations to the case of a binary with two red giants with strong winds. We find that most two-wind models on the orbital plane show a ‘double spiral’ structure close to the binary source, and that these two arms merge into a single spiral structure at larger distances. However, for the case of a binary with two identical winds, the two spiral arms are still present at large distances from the binary source. We also find that for models of two (not identical) dynamically important winds, a region close to the orbital plane has material from both winds. Also, an approximately conical region centered on the orbital axis is filled exclusively by the wind with larger momentum rate. These two structures lead to morphologies reminiscent of the so-called ‘hour glass’ planetary nebulae. Finally, we find that increasing wind velocity disparities lead to the formation of clumpy structures along the spiral arms. Observations of ‘clumpy spirals’ are therefore likely to indicate the presence of two strong winds from the stars in the central binary system.