Shear-thinning Control of Transition and Turbulent Dissipation: A Generalised Newtonian Spectral Study

This research investigates how shear-dependent viscosity affects the transition to turbulence and fully developed turbulent statistics in an inelastic, generalised Newtonian fluid governed by the Carreau-Yasuda model. To facilitate this, a pseudo-spectral solver for the two-dimensional incompressible Navier-Stokes equations was developed. By evaluating the variable-viscosity diffusion term through the divergence of the deviatoric stress, the solver exactly recovers the Newtonian limit. The method was rigorously verified against standard analytical benchmarks, achieving high precision. The study demonstrates that in a perturbed free shear layer, shear-thinning suppresses perturbation kinetic energy amplification by up to three orders of magnitude compared to a Newtonian baseline. This reduction affects both linear growth and saturation levels, becoming more pronounced at higher Reynolds numbers. In steady forced turbulence, reduced viscosity in high-strain areas sharpens the small-scale vorticity field. This shifts energy to higher wavenumbers and raises the mean enstrophy by roughly eighteen per cent. Because viscosity drops exactly where strain peaks, the dissipation field becomes significantly less intermittent. Furthermore, a dissipation-based drag metric decreases steadily as the power-law index falls, showing an 83 per cent reduction at an index of 0.4. Ultimately, the research attributes these dynamics to a single unifying mechanism, specifically a strain-gated modulation of the diffusion operator. The work thus provides valuable insights for ongoing investigations into wall-bounded generalised Newtonian flow and elasto-inertial turbulence.