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I think one thing we can say with a good bit of certainty is that the pressure reduction is not in any case the result of some kind of "preferential reduction of the perpendicular velocity components" and that it is not even easily related to molecular velocity at all in the case of liquids.
Here's what I *think* we have established:
1. The pressure field is set up during the transient phase that results in satisfying the continuity equation by the procedure described here:
https://carnot.physics.buffalo.edu/archives/2010/11_2010/msg00778.html
2. Now, because the process is adiabatic, the equation of state is barotropic and the density and temperature are both monotonically increasing functions of pressure. (i.e., less squeezing => lower density and temperature) as described here:
https://carnot.physics.buffalo.edu/archives/2010/11_2010/msg00762.html
3. Thus, the temperature will generally be lower in the low pressure regions. For a gas this will translate fairly directly into lower molecular velocities (in all directions), but they are not the *only* factor in the pressure reduction. For a liquid, the translation is less direct and the pressure reduction is mostly associated with the (very small) density reduction.
John Mallinckrodt
Cal Poly Pomona