Observationally, we find that this Newtonian or inertial frame is one in which the distant galaxies are not rotating. Some people say that the water goes down clockwise in the Southern hemisphere and anticlockwise in the Northern hemisphere. I am tempted to suggest that these people have never, or very rarely, looked. I have never noticed a correlation with the hemisphere. Here is an experiment for you to try.
Part fill it with cold water.
Once you have done so, pull out the plug and observe the direction of the water flow. Then part fill it with hot water. It is worthwhile correcting a common misunderstanding about Foucault's Pendulum. It is sometimes said that the pendulum swings in a plane which is fixed with respect to an inertial frame, or more poetically that the Earth rotates underneath the pendulum. This is true at the poles and also true for a pendulum swinging East-West at the equator.