In: Mechanical Engineering
For the flow field ?⃗ = ? + Ω × ? , where ?⃗ and Ω are constant linear- and angular velocity vectors, use index notation to find its strain rate tensor ??? and rotation tensor ???.
We have,
Now,
Thus,
Using relation for strain rate tensor and rotation tensor as shown above
where, is the component of u along i direction
is the component of along i direction