How do I sketch a flow profile and solve for curl in vector calculus?

[Darsh_22]

Homework Statement

let f(y) = v0 exp(−y^2/L2), with some constant v0 > 0. Make a sketch of the flow
profile. Determine curl v for this case and discuss strength and direction of the local
vorticity. How does shear come into play here? (Hint: Consider a small paddle wheel in
the flow)

Relevant Equations

curl of vector.

Hello,
Can someone explain how to sketch the flow profile in detail. Also, I solved for curl, but I'm getting a zero while the answer is the differentiation of the function f(y). Pls do help me out!

 

[Gordianus]

I don't see a vector field. Just a scalar function.

 

[FactChecker]

Is this supposed to be a complex function of a complex variable?

 

[Darsh_22]

this is the entire question. I did (a).

 

[Orodruin]

Please show your attempt!

 

[Gordianus]

Wikipedia quotes the divergence and curl of vector fields in cartesian, cylindrical and spherical coordinates.

 

[Darsh_22]

Please show your attempt!

this is for part B, the one I'm doubtful of. The curl is f'(y), which I don't understand how. Let me know if I'm wrong anywhere.

 

[Gordianus]

Your attempt is OK but you feel uneasy, why?

 

[Darsh_22]

Your attempt is OK but you feel uneasy, why?

Hey Gordianus,
This is the answer given by my professor and that is why I think my answer would be incorrect.
Also, I do not know how to do this linear mapping or sketch the flow profile.