I have a doubt, a sort of paradox. It is known that the classical Navier-Stokes equation in the limit of Reynolds number that goes to infinity - the high Reynolds regime - gives the classical Euler's equation (see this question for a definition of "Re" and this for the Euler limit at high Re).

Question: Since flows at a high Reynolds number become quickly fully turbulent (see this), I am wondering whether all the ideal fluids, for which Euler's equation is valid, are prone to turbulence.



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