Discussion
Consider the velocities \(u, v\), and \(w\) in x-, y-, and z-directions, respectively. The vorticity expression in the y-z plane is
Answer: C
The vorticity in the y-z plane is \(\frac{\partial w}{\partial y} - \frac{\partial v}{\partial z}\).
Rotation in the y-z plane is rotation about the x axis, so it is the x-component of \(\nabla \times \vec{V}\):
\(\omega_x = \dfrac{\partial w}{\partial y} - \dfrac{\partial v}{\partial z}\)
\(\frac{\partial v}{\partial x} - \frac{\partial u}{\partial y}\) is \(\omega_z\), rotation in the x-y plane, and \(\frac{\partial u}{\partial z} - \frac{\partial w}{\partial x}\) is \(\omega_y\), rotation in the x-z plane. \(\frac{\partial v}{\partial y} - \frac{\partial w}{\partial z}\) is a difference of normal strain rates, not a rotation.
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