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Autori principali: Zhang, Mengqi, Wan, Dongdong, Tan, Huanshu
Natura: Preprint
Pubblicazione: 2026
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Accesso online:https://arxiv.org/abs/2605.03417
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author Zhang, Mengqi
Wan, Dongdong
Tan, Huanshu
author_facet Zhang, Mengqi
Wan, Dongdong
Tan, Huanshu
contents This study investigates the influence of shear-thinning on the instability of a prototype time-periodic flow, the Stokes layer, in Carreau fluids. The time-dependent base flow was solved using a numerical method and a binomial expansion method. The expansion is conducted in terms of the nondimensional characteristic time ($Λ$), which quantifies the fluid's response time in viscosity to changes in shear rate. The expansion method shows good agreement with the numerical solution, provided that $Λ$ remains small. To understand the effect of shear-thinning on time-periodic flow instability, a Floquet analysis was conducted to examine two key parameters of the Carreau model, i.e., $Λ$ and the power-law exponent $n$. Our results show that decreasing $n$, which signifies stronger shear-thinning behavior, has a monotonic stabilizing effect on the flow within the range of investigated $n$. In contrast, increasing $Λ$ has a non-monotonic effect on the flow instability, which can be observed in both the weakly and strongly shear-thinning regimes. To clarify the instability mechanism, we perform an energy analysis showing that instability arises when the perturbation field is in phase with the oscillatory base flow, enabling efficient energy extraction from the time-dependent shear. A phase mismatch suppresses this transfer and stabilises the flow. This mechanism parallels the classical energy-production process in steady shear flows, where streamwise and wall-normal velocity perturbations exhibit a characteristic phase difference. Crucially, it is identified here for the first time in a time-periodic shear flow.
format Preprint
id arxiv_https___arxiv_org_abs_2605_03417
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Flow instability in Stokes layer of Carreau fluids
Zhang, Mengqi
Wan, Dongdong
Tan, Huanshu
Fluid Dynamics
This study investigates the influence of shear-thinning on the instability of a prototype time-periodic flow, the Stokes layer, in Carreau fluids. The time-dependent base flow was solved using a numerical method and a binomial expansion method. The expansion is conducted in terms of the nondimensional characteristic time ($Λ$), which quantifies the fluid's response time in viscosity to changes in shear rate. The expansion method shows good agreement with the numerical solution, provided that $Λ$ remains small. To understand the effect of shear-thinning on time-periodic flow instability, a Floquet analysis was conducted to examine two key parameters of the Carreau model, i.e., $Λ$ and the power-law exponent $n$. Our results show that decreasing $n$, which signifies stronger shear-thinning behavior, has a monotonic stabilizing effect on the flow within the range of investigated $n$. In contrast, increasing $Λ$ has a non-monotonic effect on the flow instability, which can be observed in both the weakly and strongly shear-thinning regimes. To clarify the instability mechanism, we perform an energy analysis showing that instability arises when the perturbation field is in phase with the oscillatory base flow, enabling efficient energy extraction from the time-dependent shear. A phase mismatch suppresses this transfer and stabilises the flow. This mechanism parallels the classical energy-production process in steady shear flows, where streamwise and wall-normal velocity perturbations exhibit a characteristic phase difference. Crucially, it is identified here for the first time in a time-periodic shear flow.
title Flow instability in Stokes layer of Carreau fluids
topic Fluid Dynamics
url https://arxiv.org/abs/2605.03417