We can get forU 21 iU21 = 1 2 ∂ ∂y [ ∂U21 ∂y + n−1 2 3( ∂U0 ∂y 2 ∂U ∗ 11 ∂y + ∂U ∗ 0 ∂y 2 ∂U13 ∂y + 2∂U0 ∂y ∂U ∗ 0 ∂y ∂U11 ∂y ) + (n−1)(n−3) 8 10( ∂U0 ∂y )3( ∂U ∗ 0 ∂y )2]

ODEs for the solutions at the order ofΛ 4 The corresponding ODEs forU 21,U 23 andU 25 are presented as follows

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Flow instability in Stokes layer of Carreau fluids

physics.flu-dyn · 2026-05-05 · unverdicted · novelty 6.0

Stronger shear-thinning (lower n) monotonically stabilizes the Stokes layer while the response time Λ has non-monotonic effects; instability occurs when perturbations phase-lock with the oscillatory base flow to extract energy.

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Flow instability in Stokes layer of Carreau fluids physics.flu-dyn · 2026-05-05 · unverdicted · none · ref 6
Stronger shear-thinning (lower n) monotonically stabilizes the Stokes layer while the response time Λ has non-monotonic effects; instability occurs when perturbations phase-lock with the oscillatory base flow to extract energy.

We can get forU 21 iU21 = 1 2 ∂ ∂y [ ∂U21 ∂y + n−1 2 3( ∂U0 ∂y 2 ∂U ∗ 11 ∂y + ∂U ∗ 0 ∂y 2 ∂U13 ∂y + 2∂U0 ∂y ∂U ∗ 0 ∂y ∂U11 ∂y ) + (n−1)(n−3) 8 10( ∂U0 ∂y )3( ∂U ∗ 0 ∂y )2]

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