Vortex potential flow with gravity
Hello everybody,
I am studying the potential flow of a vortex and I have a question. Would be really nice if somebody could help out.
Conceptually the vortex stream function is constant in z so the streamlines are perfect circles. I am not sure how to add gravity to this description. I would imagine that gravity would then cause the circles to become spirals.
I was hoping to find a function that defined the position of the particle for a given time, along this spiral line. I also wish to find the velocity function for the particle along the spiral streamline.
I looked at a few books, found pares online, but they always end their potential flow chapters before addressing this issue. And unfortunately I don't know how to solve this problem.
If anybody has seen any link that deals with this subject would be much appreciated. Thank you for your time.
Cheers,
Yara e o vento
