I just thought of a problem that seems quite fundamental but I couldn't find a clear answer or explanation.
Consider a solid sphere falling in a Newtonian fluid due to gravity. It eventually reaches its terminal vertical velocity. Now let's add a constant side wind: can this induce a net vertical force and hence increase or decrease the vertical speed of the sphere?
At low Reynolds number I believe the answer is no due to the linearity of the Stokes equation. But what about at finite Reynolds number? Even if the object falling is perfectly symmetrical, the flow around is not, possibly dramatically (e.g. recirculation zone, vortex shedding), and so it would not really surprise me if adding side wind to that situation would have an effect on the vertical direction. But intuitively I can't tell if it would indeed have an effect, and if so if it would speed up or slow down the vertical descent.