Require Help from Aeronautical Engineers, University assignment

[Tico1234]

Hi people,

I would like to kindly ask if there's anyone that can help me out with this question, Our lecturer only vaguely explained it to us without any useful information or guidelines.

Tropical Cyclone Hudhud, formally known as Cyclone 3B, is the first organized tropical system in the Bay of Bengal since the middle of May hit the sub-continental of India last month. Unfortunately, it was also subjected to north easterly wind of speeds up to 100 miles/hr. Assuming that the Cyclone 3B (Hudhud) could be represented by an Irrotational Vortex (Counterclock wise, centre at origin) which could be presented by the stream function:
ψ=-K/2π ln r
And the potential function φ= - K/2π θ

For this flow the origin is a singular point, K is the strength of the Vortex (Cyclone), Γ = K around any closed curve enclosing origin, and Γ = 0 around any closed curve not enclosing origin, And the wind could be a combination of two uniform flows.

Question
Derive expressions for the stream and potential functions of the combined flows.


We were told to add all stream functions . ψ = ψ₁ + ψ₂ + ψ₃
ψ₃ being the stream function given.

Please, Any help is greatly appreciated. (I do apologize if this isn't the right place to ask such question.)

[Kelly_Bramble]

No homework