Vector fields can be interpreted as a flow of fluids, many many tiny arrows in different directions. This brings us to divergence. Denoted , divergence represents the tendency of this vector field to flow towards a point or out from a point. The divergence, calculated as the dot product of the gradient is defined, $$
\text{Let } \vec{v} = \left[\begin{matrix}f(x,y\dots) \ g(x,y\dots) \ \vdots\end{matrix}\right]
;\text{, then } \text{div}\vec{v}=\divergence \vec{v} = \pdv{f}{x}+\pdv{g}{y}+\dots=f_x+g_y+h_z\dots
Positive divergence is when a point acts as a "source", the vector field flows away, "out from" that point. Similarly, negative divergence is when the point acts as a "drain", the vector field flows towards/into it. Zero divergence is obvious, the field is unaffected and goes in random directions or as usual. # [[87 - Curl]]