Floquet stability analysis of viscoelastic flow over a cylinder.

*(English)*Zbl 1359.76029Summary: A Floquet linear stability analysis has been performed on a viscoelastic cylinder wake. The FENE-P model is used to represent the non-Newtonian fluid, and the analysis is done using a modified version of an existing nonlinear code to compute the linearized initial value problem governing the growth of small perturbations in the wake. By measuring instability growth rates over a wide range of disturbance spanwise wavenumbers \(\alpha \), the effects of viscoelasticity were identified and compared directly to Newtonian results.

At a Reynolds number of 300, two unstable bands exist over the range \(0 \leq \alpha \leq 10\) for Newtonian flow. For the low \(\alpha \) band, associated with the “mode A” wake instability, a monotonic reduction in growth rates is found for increasing polymer extensibility \(L\). For the high \(\alpha \) band, associated with the “mode B” instability, first a rise, then a significant decrease to a stable state is found for the instability growth rates as \(L\) is increased from \(L = 10\) to \(L = 30\). The mechanism behind this stabilization of both mode A and mode B instabilities is due to the change of the base flow, rather than a direct effect of viscoelasticity on the perturbation.

At a Reynolds number of 300, two unstable bands exist over the range \(0 \leq \alpha \leq 10\) for Newtonian flow. For the low \(\alpha \) band, associated with the “mode A” wake instability, a monotonic reduction in growth rates is found for increasing polymer extensibility \(L\). For the high \(\alpha \) band, associated with the “mode B” instability, first a rise, then a significant decrease to a stable state is found for the instability growth rates as \(L\) is increased from \(L = 10\) to \(L = 30\). The mechanism behind this stabilization of both mode A and mode B instabilities is due to the change of the base flow, rather than a direct effect of viscoelasticity on the perturbation.

##### MSC:

76A10 | Viscoelastic fluids |

76E17 | Interfacial stability and instability in hydrodynamic stability |

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\textit{D. Richter} et al., J. Non-Newton. Fluid Mech. 166, No. 11, 554--565 (2011; Zbl 1359.76029)

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