旋度(curl)係向量微積分嘅一個概念,適用喺多變量向量場函數。一個多變量向量函數嘅旋度係一個多變量向量函數。旋度嘅意思係,對於投射喺一個座標平面嘅多變量純量函數,每一點嘅旋度係佢有幾傾向圍住嗰一點轉嘅指標,其中轉軸嘅方向就係旋度向量嘅方向。旋度通常寫做 ∇ × u {\displaystyle \nabla \times \mathbf {u} } 。
旋度嘅定藝要用到Nabla 算子表示。對於一個三維向量函數 u ( x , y , z ) {\displaystyle \mathbf {u} (x,y,z)} ,佢嘅旋度係:
∇ × u = | i j k ∂ ∂ x ∂ ∂ y ∂ ∂ z u x u y u z | = ( ∂ u z ∂ y − ∂ u y ∂ z ) i + ( ∂ u x ∂ z − ∂ u z ∂ x ) j + ( ∂ u y ∂ x − ∂ u x ∂ y ) k {\displaystyle \nabla \times \mathbf {u} ={\begin{aligned}{\begin{vmatrix}\mathbf {i} &\mathbf {j} &\mathbf {k} \\{\dfrac {\partial }{\partial x}}&{\dfrac {\partial }{\partial y}}&{\dfrac {\partial }{\partial z}}\\u_{x}&u_{y}&u_{z}\end{vmatrix}}\end{aligned}}=({\dfrac {\partial u_{z}}{\partial y}}-{\dfrac {\partial u_{y}}{\partial z}})\mathbf {i} +({\dfrac {\partial u_{x}}{\partial z}}-{\dfrac {\partial u_{z}}{\partial x}})\mathbf {j} +({\dfrac {\partial u_{y}}{\partial x}}-{\dfrac {\partial u_{x}}{\partial y}})\mathbf {k} }
想搞清楚旋度嘅概念,去 https://www.youtube.com/watch?v=ThxMvNPMitE&t=226s 睇下。