divergence of a vector field

The divergence of a vector field is a mathematical concept that describes the rate at which a vector-valued function is expanding or contracting at a given point. It's a differential operator applied to a three-dimensional vector field, essentially measuring the "outflow" of the field from an infinitesimal volume around that point.1

For example, in fluid dynamics, the divergence of a velocity field indicates whether a fluid is accumulating or dispersing at a certain location. If the divergence is zero, the fluid is incompressible, meaning its volume doesn't change. A vector field is a set of vectors associated with a function, where each point in the function corresponds to a vector.123