![[curl.png]] The "curl" of a vector field is a property indicating local rotation. To understand this intuitively, consider the illustration above which depects the direction field of the system $ \begin{pmatrix} \dot{x}\\ \dot{y} \end{pmatrix} = \begin{pmatrix} -\sin 2x + \cos y\\ (\cos y+2)\cos x \end{pmatrix} $ near the equilibrium point $(\frac{\pi}{2},\frac{3\pi}{2})$, which is marked with a blue dot. Imagine this field as the current on the surface of a turbulent river. If you were to gently place a flower at the point marked with the blue dot, the swirl of the current would cause the flower to rotate clockwise. This is negative curl (positive curl would cause anticlockwise local rotation). The field illustrated above is classified as a "spiral source" because as well as non-zero curl it has positive [[Divergence|divergence]] as can be seen from the arrows "sourcing out" from the equilibrium point.