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

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Homework Help Overview

The discussion revolves around sketching a flow profile and solving for curl in the context of vector calculus. Participants are exploring the relationship between vector fields and scalar functions, as well as addressing specific calculations related to curl.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are questioning the nature of the function being analyzed, with some suggesting it may be a scalar rather than a vector field. Others are uncertain about the implications of the curl being zero and its relation to the differentiation of a function.

Discussion Status

The discussion is active, with participants sharing their attempts and expressing doubts about their understanding. Some have provided insights into the definitions of divergence and curl, while others are seeking clarification on specific aspects of the problem.

Contextual Notes

There is mention of a professor's answer that may differ from participants' calculations, leading to confusion. Additionally, there are references to linear mapping and the need for a detailed sketch of the flow profile, indicating potential gaps in information or understanding.

Darsh_22
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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!
 
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I don't see a vector field. Just a scalar function.
 
Is this supposed to be a complex function of a complex variable?
 
1637669712566.png

this is the entire question. I did (a).
 
Please show your attempt!
 
Wikipedia quotes the divergence and curl of vector fields in cartesian, cylindrical and spherical coordinates.
 
Orodruin said:
Please show your attempt!
1637671753028.png


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.
 
Your attempt is OK but you feel uneasy, why?
 
Gordianus said:
Your attempt is OK but you feel uneasy, why?
1637678088124.png

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.
 

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