The wikipedia article on divergence describes one interpretation of divergence: "The velocity of the air at each point defines a vector field. While air is heated in a region, it expands in all directions, and thus the velocity field points outward from that region."
If we have a vector field which represents a force, I interpret the divergence as representing the strength of the field at whatever point it's taken at. However I'm confused on how to interpret the divergence of a velocity field. Clearly if the divergence is positive gas is expanding outward and if it's negative it's contracting, however what quantity is actually represented?
If I have a velocity field with $m/s$ units, then the div presumably has $m/s^2$ units. Is the quantity we get the actual acceleration of gas away from that point?
Best Answer
I believe the derivative in the divergence operator is with respect to space, not time, therefore the unit is expected to be 1/s, not m/s^2. So it is not the acceleration, but frequency. I am not sure about the physical interpretation of that though.