I'm not sure I see this the same way you do. It all looks the same direction to me.

However, it is possible for winds to go different directions at different heights. It's also common to get quite marked interfaces between warm and cold, or moist and dry air. Not quite like oil and water, but these layers and banks of air slide over and under each other in a similar way - showing a reluctance to mix which results in the patterns one sees in clouds.

I am no climatologist, but from that rather lovely picture I get the impression of winds blowing in at least four directions. Actually I think it is likely that two of those "directions" simply represent air bodies, either with one travelling faster than the other in the same direction, or one stationary, either of which situations may be regarded as two winds in tangent, travelling in opposite directions relative to each other. Pete has rightly described some of the variety of ways in which moving air can create simultaneous winds blowing in different directions. For such winds to create visible effects in the form of clouds, it often requires either air bodies in contact, where clouds form at the interfaces, or a rising or sinking, with clouds forming at the peak of the motion. Giant ripples in flowing air commonly create herringbone clouds through such processes.

To me personally, the two wool-carding effects in your picture look like the consequence of a higher body of air skidding fairly smoothly over a lower body. A slight difference of incidence, or alternatively, of relative velocities, could explain the difference between the two halves of those woolly bars.

Just an impression, I must emphasise!

Cheers

Jon