What does "downshear" mean? I occasionally read descriptions such as "downshear of the vortex" in meteorological publications.
What does this mean?
 A: In meteorology, the shear vector is typically calculated as the vector difference of the wind aloft minus the wind below (often using layer averages), much of which is further detailed here.
The reason this usage is heavy in meteorology stems from the fact that the vortices being talked about are often at the storm scale; features like tornadoes, mesocyclones, and supercells.  A very important mechanism in the development of these rotations is the generation of streamwise vorticity due by this vertical variation, or shear, of the environmental wind, as discussed in Davies-Jones 1984.
Upshear thereby means occurring against this shear vector.  Upshear and downshear can often be used in describing the development of the cold pool and  updrafts, and relates to how storms (and thus their vortices) evolve.  This page offers very quality descriptions of how storms may interact with the shear vector.  
A: "Downshear of the vortex"? 
And your link is just a google search for these words.
-But as Vortex doesn't have too much shear stresses, 

it must mean this bottom flow which connects/feeds the low pressure vortex center with fluid. 
Please note that it doesn't make any difference if the fluid is going away from the bottom or from the top of the vortex. (Same video at 11:00)

I have coloured quite complete videos available here, in this play list
Start at 5:00 in this video,,
