Fluid Mechanics is a branch of physics that uses a lot of vector calculus in $\mathbb{R}^3$ to describe phenomena mathematically. Calculus on manifolds, however, is the straightforward generalization of vector calculus and has a lot of interesting and useful tools like differential forms, lie derivatives, flows of vector fields and so on.

Is there some book/article that treats fluid mechanics using calculus on manifolds? I've searched a lot for some book like this but I could only find one called "A mathematical introduction to fluid mechanics" which although uses a lot of math restricts itself to vector calculus. Is there some other book that uses the tools of the calculus on manifolds to describe fluid mechanics phenomena?