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We were being given intro to fluid dynamics at our school

So the thing that sparked me up is $ g$ in expression of:

Static pressure of fluid

Bernoulli Principle

I am curious how fluids(especially liquids) will behave when they are near or at strong gravitational fields and when they approach

near-implies--> You may not be on the body but within distance $\epsilon$ such that $g$ of the body is not quite appreciably different from the maximum acceleration due to gravity of body.

approach-implies--> AT some distance such that $g$ is increasing gradually or at some certain rate/

I suspect as the liquid approaches it may turning rigid.Something like the rate at which it turn rigid or loses it properties of fluid/liquid.This rate may affect quite of its properties(sorry i don't mathematical background or graduate physics background..I can only speculate as high school studentt)

But the things is this may be only the case for uber-strong gravitational fields such as those of blackholes

But what about massive structure?(think of stars having millions times mass than sun..exaggertaion?) which may not have $g$ like black holes but they are appreciably strong?

Since the strong gravitational field brings appreciable compressability therefore things like Bernouili might not be applicable

What incites me more is whether fluid(mainly liquids) will have different demeanour with boundary(as in contained in some container) and without boundary

Will the geometery of boundary affect fluid?

I know this situation will be titled as illegal use of artistic licences at PhysSE but who know what potential-eenrgy black magic may craft dark things out there in wild universe out there.

Envision a situation that $g$ is changing with respect to time and periodic then how liquid might behave(think of a massive body passing near fluid for certain period of time after a certain interval)

These are some of things that buggs me for now

Can somebody enlighten us on this?

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  • $\begingroup$ You are correct in saying that instrong g field, bernoulli will become incorrect, since this law governs incompressible fluid flow. But i will need to look up exactly how stuff will change in this situation. $\endgroup$ – Lelouch Dec 11 '16 at 16:24
  • $\begingroup$ You may be interested in the Rayleigh-Taylor instability (I imagine there are plenty of YouTube videos that show the instability). $\endgroup$ – Kyle Kanos Dec 11 '16 at 19:32
  • $\begingroup$ @Lelouch:Have you cam across any such thing? $\endgroup$ – Xasel Dec 12 '16 at 12:12
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A lot of work has been done in relativistic hydrodynamics and fluid dynamics, as well as relativistic kinetic theory. Both for special and general relativity. A couple reviews are below, and you'd get a general idea, but it's not straightforward.

Relativistic fluids are used to model matter and radiation in dense and collapsing stars (neutron stars, black holes collapsing), and that includes then how they behave in a gravitational field which they also create. So it is a very nonlinear problem. It is also used for instance to model cosmology, the matter and radiation density, pressure and shear/stress of the matter and radiation in the universe, in large scale. From that we know for instance how the cosmological expansion of the universe affects the matter and radiation densities over time.

In strong gravity, i.e. General Relativity, it is not easy to solve for any complicated fluid models, so usually one picks equations of state (density as function of pressure and temperature for instance, in the fluid, dependent on what kind of fluid it is) to model,it, and can get some analytical and if not numerical solutions. One of the earliest models of collapse is the TOV equation (you can google it) for collapse, where they assumed a pressureless fluid. For effects like turbulence it is hard to obtain analytical solutions, and so they tend to be numerical ones or small perturbations off a base solution.

https://arxiv.org/pdf/gr-qc/0603009.pdf

http://relativity.livingreviews.org/Articles/lrr-2007-1/download/lrr-2007-1Color.pdf

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