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

Articles in Press

Document Type : Research Paper

Author
Ashish Gad
Department of Mechanical Engineering, The Engineering College, Monk Ferry, Birkenhead, CH41 5LH, United Kingdom
10.22055/jacm.2026.49533.6054
Abstract
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-reduction metric decreases steadily as the power-law index falls, by up to about 83 per cent at an index of 0.4. While the reduction of viscosity in high-strain regions is a direct property of the shear-thinning model, the new understanding obtained here lies in its net effect on the turbulent structure: the small-scale vorticity and the dissipation field respond in opposite directions, the former becoming finer while the latter becomes smoother. The work thus provides verifiable insight for ongoing investigations into wall-bounded generalised Newtonian flow and elasto-inertial turbulence.
Keywords
Shear-thinning fluid
Generalised Newtonian fluid
Carreau&ndash
Yasuda model
Pseudo-spectral method
Transition to turbulence
Subjects

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Available Online from 11 September 2026