The sketch to the right depicts the velocity profile in
a simple shear flow. The fluid is moving to the right
and the magnitude of the fluid velocity increases linearly
with y. The velocity can be written
where C is a constant determining the slope of the profile. 
To make the analysis a little easier, we consider the flow
as it would be observed by someone moving with the velocity of point P.
This person sees velocity profile to the right.

The rotational field is depicted in the following sketch. On the left, the velocity vectors are drawn at selected points. On the right the streamlines of the flow are shown.
In this purely rotational flow all fluid elements experience solid body rotation. In other words the fluid elements rotate without undergoing any deformation. The motion is simulated with the following animation. Press the triangle in the lower left corner to begin the animation.
The deformation field is depicted in the following sketch. On the left, the velocity vectors are drawn at selected points. On the right the streamlines of the flow are shown.
The deformation velocity field initially appears to be quite complex. The flow approaches point P from the upper left and lower right corners. It moves away from point P toward the upper right and lower left corners. The green lines are asymptotes for the approaching and leaving flow directions. These lines are also the principle directions of the deformation flow. Fluid elements oriented along the principle directions experience pure extensional strain. This motion is depicted in the following animation. The fluid elements shown as yellow boxes are initially aligned with the principle directions. Press the triangle in the lower left corner to begin the animation.
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