"Gravity as a fluid dynamic phenomenon in a superfluid quantum space. Fluid quantum gravity and relativity." (2015) https://hal.science/hal-01248015/
TLDR; In SQS (Superfluid Quantum Space), Quantum gravity has fluid vortices with Gross-Pitaevskii, Bernoulli's, and IIUC so also Navier-Stokes; so Quantum CFD (Computational Fluid Dynamics).
That article describes a hypothetical microphysical model of gravity. It's an old idea which has been done better by others (see e.g. "The Universe in a Helium Droplet" [1]). Whether right or wrong, it has no bearing on your claim that
> Gravity, arguably, does not experience gravity as a curved surface.
Any valid microphysical model of gravity must be able to reproduce the successes of general relativity in the classical limit, including the ability to match the shape of gravitational waves produced by black hole mergers. So if you want to argue that gravity "does not experience gravity as a curved surface", you have two options:
1) show that the non-linear (i.e. self-interaction) terms of Einstein's equations do not involve curvature or
2) come up with an alternative theory of gravity which does not reduce to general relativity in the classical limit and yet manages to reproduce all its successful predictions.
Which one is it?
[1] https://academic.oup.com/book/11557
[1] (2009) Does not disprove hydrodynamic SQS theories of quantum gravity.
A table of predictive error per experiment,{parameters},model might help us understand.
SQS purports to describe black hole internal topology where others do not. GR does not describe the internal topology of merging black hole vortices. Various theories of Quantum Gravity (QG) attempt to reconcile Dirac's pre-"Dirac sea" antimatter claims.
A unified model must: differ from classical mechanics where observational results don't match classical predictions, describe superfluid 3Helium in a beaker, describe gravity in Bose-Einstein condensate superfluids , describe conductivity in superconductors and dielectrics, not introduce unoobserved "annihilation", explain how helicopters have lift, describe quantum locking, describe paths through fluids and gravity, predict n-body gravity experiments on earth in fluids with Bernoulli's and in space, [...]
What else must a unified model of gravity and other forces predict with low error?
Why do I like Fedi's (2015/2016)? IDK. Maybe it's the abstract, maybe it's that nothing else even tries to do fluids and Bernoulli's. N-body gravity solutions with fluid vortices should predict all existing numerical n-body outcomes?
That so many things in space look fluidic - how many spiral arms are there on a nebula, all existing visual representations of black holes look like fluids, merging neutron stars look like emergent patterns from curl, too
Somehow I doubt anyone has even yet left an evolutionary algorithm online even all night to mutate and crossover the expression tree(s) to minimize predictive error according to existing experimental observations