渦度
渦度は、速度勾配テンソルの反対称成分
( ∂ [ i v j ] ) = 1 2 ( 0 ∂ v 1 ∂ x 2 − ∂ v 2 ∂ x 1 ∂ v 1 ∂ x 3 − ∂ v 3 ∂ x 1 ∂ v 2 ∂ x 1 − ∂ v 1 ∂ x 2 0 ∂ v 2 ∂ x 3 − ∂ v 3 ∂ x 2 ∂ v 3 ∂ x 1 − ∂ v 1 ∂ x 3 ∂ v 3 ∂ x 2 − ∂ v 2 ∂ x 3 0 ) {\displaystyle {\big (}\partial _{[i}v_{j]}{\big )}={\frac {1}{2}}{\begin{pmatrix}0&{\dfrac {\partial v_{1}}{\partial x_{2}}}-{\dfrac {\partial v_{2}}{\partial x_{1}}}&{\dfrac {\partial v_{1}}{\partial x_{3}}}-{\dfrac {\partial v_{3}}{\partial x_{1}}}\\\\{\dfrac {\partial v_{2}}{\partial x_{1}}}-{\dfrac {\partial v_{1}}{\partial x_{2}}}&0&{\dfrac {\partial v_{2}}{\partial x_{3}}}-{\dfrac {\partial v_{3}}{\partial x_{2}}}\\\\{\dfrac {\partial v_{3}}{\partial x_{1}}}-{\dfrac {\partial v_{1}}{\partial x_{3}}}&{\dfrac {\partial v_{3}}{\partial x_{2}}}-{\dfrac {\partial v_{2}}{\partial x_{3}}}&0\end{pmatrix}}}