Question

How does gravity affect hydrodynamics?

Answer 1

There are two things. Gravity waves and gravitational waves. See explanation below

Explanation:

Gravity waves are waves produced at the interface between two surfaces in a fluid. An example is the surface of the ocean. Wind causes ripples which propagate. Gravity waves are transverse waves. The water surface moves vertically on a horizontal surface.

Gravitational waves are waves produced by two massive objects like stars when each accelerates in the gravitational field of the other. They arise as solutions to the linearized approximation of Einstein's equations. These are waves in spacetime, and they lead test particles forming a circle to be squeezed in one direction then other, oscillating between ellipses along the x then the y axis.