What are the proper words for explaining physically the free stream boundary condition?

Dear Tao

I haven't an exact way to explain it physically.

As you should allways have to fix BC in your formulations, it is very usefull (from analytical point of view) to use infinity as a "point" to fix a BC. There, according to the equations you have, you can easily (+/-) fix a behavior for the magnitudes you are calculating.

Nevertheless, from a numerical point of view, the infinity could be practically unaccesible. So, you need to use a kind of BC that allows the system behaves driven by the present physical mechanisms and that is why you impose a free stream BC (or open BC); because you HAVEN'T A WAY (PHYSICALLY SUSTAINED) TO FIX A BEHAVIOR FOR YOUR VARIABLES AT THAT COORDINATES.

In this case FREE means 'I let the system do whatever it want'. Therefore, I think the physical interpretation of your imposed "free stream BC" comes from the evolution of your system at those points and the adaptability of your numerical BC to match the physical mechanisms you have to deal with at those points.

Regards

Kike