I know that when you walk through the air you form a wake vortex and turbulent air behind and the vortex grows the faster you walk. When I walk past people I almost feel wind that's behind them. So why do I feel wind behind a person when they walk by? Is it the turbulence causing the wind?
In practice, yes, but you wouldn't even need that: the simple fact that an obstacle pass through the air makes it push apart in front then sucked together on the rear, causing motion on the sides. But such viscous flow displacement would exist only close to the object, while wakes can be very long (see for instance behind cars, when there is some smoke or fog around).