point   is the scalar expression 

This expression is also called , denoted by .

EXAMPLE 1: The following vector fields represent the velocity of a gas flowing in the  . Find the circulation density of each vector field and interpret its physical meaning Figure below displays the vector fields.

(a) Uniform expansion or compression: 

(b) Uniform rotation: 

(c) Shearing flow: 

(d) Whirlpool effect: 

(a) Uniform expansion: 

(b) rotation: 

(c) Shear:

(d) Whirlpool:

divergence (flux density)

DEFINITION The   of a vector field  at the point   is 

EXAMPLE 2: Find the divergence, and interpret what it means, for each vector field in Example 1 representing the velocity of a gas flowing in the