Nonmodal amplification of stochastic disturbances in strongly elastic channel flows

Abstract

Nonmodal amplification of stochastic disturbances in elasticity-dominated channel flows of Oldroyd-B fluids is analyzed in this work. For streamwise-constant flows with high elasticity numbers $\mu$ and finite Weissenberg numbers $We$, we show that the linearized dynamics can be decomposed into slow and fast subsystems, and establish analytically that the steady-state variances of velocity and polymer stress fluctuations scale as $O(W{e}^2)$ and $O(W{e}^4)$, respectively. This demonstrates that large velocity variance can be sustained even in weakly inertial stochastically driven channel flows of viscoelastic fluids. We further show that the wall-normal and spanwise forces have the strongest impact on the flow fluctuations, and that the influence of these forces is largest on the fluctuations in streamwise velocity and the streamwise component of the polymer stress tensor. The underlying physical mechanism involves polymer stretching that introduces a lift-up of flow fluctuations similar to vortex tilting in inertia-dominated flows. The validity of our analytical results is confirmed in stochastic simulations. The phenomenon examined here provides a possible route for the early stages of a bypass transition to elastic turbulence and might be exploited to enhance mixing in microfluidic devices.

46 pages, 15 figures, to appear in J. Non-Newtonian Fluid Mech

References in corpus (6)

• Elastic turbulence in a polymer solution flow
• Efficient Mixing at low Reynolds numbers using polymer additives
• Elastic turbulence in curvilinear flows of polymer solutions
• Two-dimensional elastic turbulence
• Elastic turbulence in von Karman swirling flow between two disks
• Frequency responses of streamwise-constant perturbations in channel flows of Oldroyd-B fluids

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• Vorticity amplification in viscoelastic channel flows with long-wave surface distortions
• Splitting of localized disturbances in viscoelastic channel flow
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• Characterizing Elastic Turbulence in Channel Flows at Low Reynolds number