Variance amplification in channel flows of strongly elastic polymer solutions

Mihailo R. Jovanovic, Satish Kumar
2009 2009 American Control Conference  
This paper identifies a new mechanism for amplification of stochastic disturbances in channel flows of strongly elastic polymer solutions. For streamwise constant flows with high elasticity numbers µ and non-vanishing Reynolds numbers Re, the O(µRe 3 ) scaling of the variance amplification is established using singular perturbations techniques. This demonstrates that large variances can be maintained in stochastically driven flows occurring in weak inertial/strong elastic regimes.
more » ... , the amplification arises due to nonnormality of the governing equations and, physically, it is caused by the stretching of the polymer stresses by the background shear. The reported developments provide a possible route for a bypass transition to 'elastic turbulence' and suggest a novel method for efficient mixing in micro-fabricated straight channels. ). amplification (i.e., the H 2 norm) with the Reynolds number Re was recently developed in Ref. [6] , where f and g denote the Re-independent functions. This extends the Newtonian-fluid results [7], [8] to channel flows of viscoelastic fluids. In this paper, in order to gain insight into the conditions under which strong elasticity amplifies stochastic disturbances, we apply singular perturbation techniques to show that the variance amplification scales as E(k z ; Re, β, µ) ≈f (k z ; β)Re +ĝ(k z ; β)µRe 3 , µ 1.
doi:10.1109/acc.2009.5160632 dblp:conf/amcc/JovanovicK09 fatcat:x2qb5f5ucjc5fivqz26sggntqi