Now we consider the case of angular deformation. There is no volume change, so the velocity field has zero divergence (
). There is also no rotation of any material element of the flow, so the vorticity is zero, which implies that the vector field has to satisfy
As a result, the vector field has the form
and
where
and
are constants. The part of the vector field multiplied by the constant
gives only pure strain. Therefore, a vector field which has angular deformation as its main effect has the form
and
As an example of a vector field that only causes angular deformation to a material element of the flow, consider the case where the constants
assumes the values
.
To illustrate the effect of this velocity field to a material contour, the user can use the vector field manipulation application. Type
in the text box Input
and type
in the text box Input
. Then input in the display area, by mouse clicking, a square contour. Then change the value of time in the text box Input t, and then click the Draw button. As a result the contour suffers angular deformation by the vector field. Repeat it as many times you want. Notice that strain is also observed.