I have some questions regarding inviscid flow past solid objects.
I am studying fluid mechanics. Right now I am on inviscid flow and I am having some difficulties in understanding certain aspects of flow past solid objects. I have tried to sketch my understanding so far along with the particular issues I have below.
So the setup is that we have uniform flow at infinity and a solid non moving finite object in the way. Now from Kelvin's theorem we can show that on streamlines which go from infinity to infinity the vorticity vanishes. If these are the only streamlines the vorticity vanishes everywhere and the flow is a potential flow. However if we solve the problem under the assumption of potential flow we encounter d'Alembert's paradox. There is no drag on the body and the solution is unphysical.
There is a loophole in the argument that shows the flow is potential namely it does not apply for streamlines which hug the solid surface. Since these don't start from infinity they also don't affect the boundary conditions at infinity. So we can create additional solutions by superimposing potential flow solutions with these ones. But we then have to relax the potential flow criteria. Here are my questions:
These solutions, that include streamlines that hug the surface, have the phenomenon of separation. The streamlines lines only follow the surface partly and then partway from it. Why is speration necessary? I mean what about streamlines that go all the way around the surface of the solid body.
Also there is in these cases the formation of a surface of tangential discontinuity where the tangential component of the velocity field suffers a discontinuity. I can't seem to visualize this surface. Like where is this formed on the body itself or in the fluid bulk surrounding the body. My book says the discontinuity on the surface causes part of the fluid to have vorticity. I don't understand this and I don't understand why is the formation of said surface a necessary consequence of seperation.
There are multiple different solutions corresponding to the above problem if you take into account the multiple possible surfaces of discontinuities.
These solutions are unstable owing to the discontinuity in velocity.
Please help me answer these questions.