Fig 1. Leeside eddy
Wind blowing over the brink of a dune can create an eddy current ('recirculation cell') in the lee of the dune. If the wind is perpendicular to the brink, the eddy current is a 'roller'; if oblique, the eddy is generally helical, though of course these are idealizations -- actual eddies are driven in a complex manner by gusty wind and chaotic turbulence.
Streamers in the photos below make visible the wind direction as low-speed wind (unable to move sand) flows over the brink of a dune (Great Sand Dunes National Monument, Colorado).
Fig 2. Streamers in leeside eddy, viewed from brink level
Fig 3. Streamers in leeside eddy, viewed from top of dune
Even in conditions of strong transverse wind, the surface of the leeside slope can be relatively calm. It is common to find light organic matter (eg., dessicated seed husks and sprouts) resting on the lee slope, stirred only occasionally by turbulence.
Refer to video recordings during high-wind for examples of:
Mobilized grains on the lee slope will of course be affected by the slope; their path will be deflected downhill; thus ripples forming on the lee slope will generally not have crests aligned perpendicular to the wind.