Why is there no turbulence in the flow of spacetime around black holes? How does this flow differ from typical physical flows described by the Navier-Stokes equations with friction, or even the frictionless flows described by Euler and Bernoulli?
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Spacetime doesn’t flow in general. It has no velocity in general nor does it have viscosity. So the concept of turbulence doesn’t apply in general.
There is a “river model” which only applies to static spherically symmetric spacetimes. This model does not generalize. In this model the geometry is so simple that there cannot be any turbulence.
