Divergence is a vector operator that represents the volume density of the outward flux of a vector field.
Divergence takes in a vector-valued function
Divergence
For a vector function
, its divergence is
Intuition of Divergence
Intuitively, the divergence measures “how much a vector field is a source or a sink.” For example, in the below diagram, the divergence is
The divergence would also be positive if the vector field passing through it is speeding up:
Linking Divergence Definition to Intuition
How does the divergence definition leads to change of volume density? Say we have a 2D function
And the formula for its divergence is the following:
Let’s focus on the
Suppose
The observation can also generalized to
And divergence adds contributions of all the axis together: