Question

Describe a flow with non-zero curl and negative divergence. Provide a common example of when this type of flow occurs.

Answer 1

Curl of a flow field represents tendency of rotation present in our fluid flow, it defines rotation locally and for infinitesimal fluid element. When fluid element rotates about its centre of mass, it's called rotational flow.

A sink is a point in a flowfield where the fluid is converging into, and sink is supposed to have negative divergence, since divergence is measure of flux, negative divergence represents a converging flow.

In image above, at O (origin) there is a sink and the divergence for the flow velocity vector here will be negative as the net flux of flow is negative.

For a newtonian fluid, for example at a drain, the fluid spirals into the drain, the viscosity present in the fluid gives it a non-zero curl and the divergence at the drain is negative.

Another example can be fluid flowing inside a boundary layer near a solid surface, flow is rotational there i.e non-zero curl and if the solid surface is an adsorbent, the divergence will be negative.

BUT for an inviscid fluid in a sink flow(from above used image), the fluid vorticity is Zero even though we have circulation present.(https://physics.stackexchange.com/questions/302811/why-is-this-vector-field-curl-free)