Variable Viscosity Enables Energy Transfer Across Scales in Non-Newtonian Turbulent Flows
Researchers using direct numerical simulation have shown that in fluids with variable viscosity, the viscous term in the Navier-Stokes equations can actively transfer energy across scales — a role previously thought exclusive to convective nonlinearity. The study examined homogeneous isotropic turbulence in generalised Newtonian fluids modeled by the Carreau constitutive model, covering both shear-thinning and shear-thickening regimes. This challenges a foundational assumption in turbulence theory and may help explain anomalous spectral behavior observed in complex fluids.
A new preprint posted to arXiv investigates how energy moves across length scales in turbulent flows of fluids whose viscosity changes with shear rate, such as polymer solutions, blood, or certain industrial fluids. Using direct numerical simulation of homogeneous isotropic turbulence, the authors find that the variable viscosity term in the Navier-Stokes equations becomes nonlinear and generates a convolution product in spectral space — formally mirroring the convective term. This means the viscous contribution carries both energy dissipation and conservative energy transfer components, which are entangled and cannot be cleanly separated as in constant-viscosity fluids. The study introduces novel computations of a viscous momentum coupling function that reveals two distinct spectral regions: a sign-definite dissipative region and a transfer-like dipole structure in shear-thickening fluids that satisfies approximate antisymmetry, the hallmark of conservative energy transfer. In shear-thickening fluids, this viscous energy transfer participates in the forward energy cascade alongside convective transfer and eventually dominates in the dissipation range, replacing the classical exponential spectral cutoff with a power-law decay. The findings broaden the theoretical understanding of turbulent energy cascades by demonstrating that cross-scale energy transfer is not the exclusive province of inertial (convective) nonlinearity.
What's missing
As a preprint, this work has not yet undergone formal peer review. It remains an open question how these findings extend to anisotropic, wall-bounded, or inhomogeneous turbulent flows. The practical Reynolds number range explored and the sensitivity of results to the specific Carreau model parameters are not detailed in the abstract, leaving the generality of the conclusions to be assessed upon full review.
What different sources said
- arXiv physicsCenter
No need to stay positive: a practical approach to direct numerical simulations of elastic turbulence
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