Stagnation point

A stagnation point of a fluid flow is a point at which the velocity field vanishes. For a two-dimensional streamfunction, it is a critical point satisfying both first spatial derivatives of the streamfunction equal to zero.

A regular axisymmetric irrotational flow near a stagnation point on an impermeable tangent plane has equal tangential strain rates. The incompressibility condition forces the normal rate to be their negative double. Thus the leading velocity potential has the displayed quadratic form. Its streamline invariants are the azimuth and $z(x^2+y^2)$; for incoming flow from positive $z$, $W>0$.