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# Preturbulence in momentum-relaxing Navier-Stokes hydrodynamics

Mar 2023

In a hydrodynamic regime of electronic fluids, the electron scattering onimpurities and phonons inhibits the development of oscillating preturbulentphenomena (such as the K\'arm\'an vortex shedding) and enforces a laminar flow.Working in a local generalization of the Navier-Stokes hydrodynamics ofincompressible two-dimensional fluids, we show that the critical relaxationtime separating these two regimes is described by a surprisingly simplefractional power function of the Reynolds number. The critical exponent,$\alpha \simeq 4/3$, sets particular experimental conditions for theobservation of preturbulent effects in electronic fluids.

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