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Nonmodal amplification of stochastic disturbances in elasticity-dominatedchannel flows of Oldroyd-B fluids is analyzed in this work. Forstreamwise-constant flows with high elasticity numbers $\mu$ and finiteWeissenberg numbers $We$, we show that the linearized dynamics can bedecomposed into slow and fast subsystems, and establish analytically that thesteady-state variances of velocity and polymer stress fluctuations scale as $O(We^2)$ and $O (We^4)$, respectively. This demonstrates that large velocityvariance can be sustained even in weakly inertial stochastically driven channelflows of viscoelastic fluids. We further show that the wall-normal and spanwiseforces have the strongest impact on the flow fluctuations, and that theinfluence of these forces is largest on the fluctuations in streamwise velocityand the streamwise component of the polymer stress tensor. The underlyingphysical mechanism involves polymer stretching that introduces a lift-up offlow fluctuations similar to vortex tilting in inertia-dominated flows. Thevalidity of our analytical results is confirmed in stochastic simulations. Thephenomenon examined here provides a possible route for the early stages of abypass transition to elastic turbulence and might be exploited to enhancemixing in microfluidic devices.

Nonmodal amplification of stochastic disturbances in strongly elastic channel flows