Who says we can't? It just needs open eyes and an open mind.
To understand the picture below, keep these things in mind:
- If the streamlines are packed together, the flow speed is higher while pressure is lower than ambient.
- Conversely, when the streamlines are spaced wide apart, flow speed is lower but pressure is higher.
- Converging stream lines mean accelerating flow.
- Diverging streamlines mean the flow slows down.
Somehow, the air has to flow around the obstacle that the airfoil represents in a closed wind tunnel. It does so by speeding up (at least in subsonic flow). Conversely, when the airfoil tapers towards the trailing edge and an angle of attack makes the cross section downstream become wider, the air slows down in order to fill the available space. In the end, the mass flow near the suction peak where the cross section left open by the airfoil is narrowest is equal to that near the trailing edge when the cross section has become much larger. The same happens on the lower side: All the air passing below the stagnation line has to squeeze through the gap left between trailing edge and tunnel wall. This is only possible by a large change in speed.
Now have a look at stream lines in a windtunnel. Note that the lines near the upper and lower edge of the picture are almost straight and nearly follow the wall contour of the tunnel (picture source):
The downwash is the downward-pointing part of the streamlines over the rear part of the upper airfoil contour. Due to tunnel wall interference, the flow on the lower side near and especially past the trailing edge is very different from free flow and the air has to speed up to flow through the gap left between the airfoil and the tunnel wall.
You also see the smoke lines past the trailing edge fan out: The flow near the center section of the tunnel is still fast and stays near the bottom while the flow near the wall slows down and bends upwards, causing the lines to spread out. The lines near the wall even intersect the ones near the center! Clearly, this is a 3D effect which resembles the wake rollup past a wing in free flow, but crippled by the proximity of the tunnel wall.
While the air coming off a wing in free flight with attached flow has approximately the same speed over the whole height, here tunnel wall blockage means that the air coming off the lower side is much faster than air coming off the upper side. This is necessary to let the air shift downwards past the airfoil, as it does in the wake of a wing. Of course, the tunnel wall and friction will limit that downward movement, but by adjusting flow speed the tunnel airfoil is able to create a downwash, too.
Another way to look at it: The slow, high pressure air coming off the upper side of the airfoil squeezes the fast, low pressure air coming off the lower side down. Either way, downwash is the result.
The downwash is right there and hard to overlook: The streamlines coming off the airfoil clearly have a downward direction. Wake rollup is also happening, albeit near the right edge of the picture and less pronounced than in free flight. If that is not evidence enough, I don't know what ever will be.
The picture has to be sufficient. Sorry, no movie.