Expansion and Divergence
Expansion and Divergence
Imagine a moving fluid that may possibly expand or contract, such as a gas. Each point has a velocity vector, making all the points into what is called a vector field. At each point in the flow, the divergence of a vector field indicates the relative rate of expansion of the flow. The divergence can be visualized as follows. Near a selected point, let there be a given small cubical volume containing the point. As time changes, the volume will change shape and magnitude. The relative change in volume will be roughly proportional to the divergence of the vector field and the amount of time elapsed. Indeed, the divergence is equal to the limit of as the change in time approaches zero.
ΔV/V
ΔV/V
Δt
Δt