Mixing layer instability and vorticity amplification in a creeping viscoelastic flow

Abstract

We report quantitative evidence of mixing-layer elastic instability in a viscoelastic fluid flow between two widely spaced obstacles hindering a channel flow at Re 1 and W i 1. Two mixing layers with nonuniform shear velocity profiles are formed in the region between the obstacles. The mixing-layer instability arises in the vicinity of an inflection point on the shear velocity profile with a steep variation in the elastic stress. The instability results in an intermittent appearance of small vortices in the mixing layers and an amplification of spatio-temporal averaged vorticity in the elastic turbulence regime. The latter is characterized through scaling of friction factor with W i, and both pressure and velocity spectra. Furthermore, the observations reported provide improved understanding of the stability of the mixing layer in a viscoelastic fluid at large elasticity, i.e. W i 1 and Re 1, and oppose the current view of suppression of vorticity solely by polymer additives.

Elastic Alfven waves in elastic turbulence

“…Strikingly, an indication of the elastic waves, in numerical studies, originates from observed frequency peaks in the velocity power spectra above the elastic instability 12,13 . Analogous frequency peaks in the power spectra of velocity and absolute pressure fluctuations above the instability were also reported in experiments of a wall-bounded channel flow in a creeping viscoelastic fluid, obstructed by either a periodic array of obstacles 14 or two widely-spaced cylinders 15,16 . These observations were in agreement with numerical simulations 17 and were associated with noisy cross-stream oscillations of a pair of vortices engendered due to breaking of time-reversal symmetry.…”

Drag enhancement and drag reduction in viscoelastic flow

“…Re = 0.005, Wi = 74) and at higher Re small scale vortices emerge with an intermittent and random dynamics (e.g. Re = 0.03, Wi = 444) that constitute the ET regime [11], whereas in DR regime (e.g. Re = 0.57, Wi = 8438) much smoother spatial scale and less vortical motion are found (bottom panel of Fig.…”

“…One notices the drag reduction for El = 2433 occurs at Re ≈ 0.5 and Wi ≈ 1216, and continues till the flow relaminarizes. algebraic decay in both the power spectra of velocity and pressure fluctuations with the exponents >∼ 3 (see further), and intensive vorticity dynamics and a growth of average vorticity asω ∼ Wi 0.2 and f /f lam ∼ Wi 0.2 − typical for ET[11]. For low El, either a saturation or reduction of the friction factor with Re or Wi marks the DR regime.…”

“…The two vortices constitute two mixing layers with a non-uniform shear velocity profile filling the inter-obstacle space. Further increase of Wi leads to chaotic dynamics with properties similar to ET [11]. There are several reasons for the choice of the flow geometry: (i) Since blockage ratio D/w 1, the flow between the cylinders is unbounded, like "an island in a sea" of otherwise laminar channel flow, contrary to all previous wall-dominated flow geometries that were used to study ET (D and w are the cylinders' diameter and channel width, respectively) [3,[5][6][7][8][9].…”

“…ET is a spatially smooth, random in time chaotic flow, which statistical, mean and spectral properties are characterized experimentally [3,[5][6][7][8][9][10][11], theoretically [12,13] and numerically [14][15][16][17]. The hallmark of ET is a steep power-law decay of velocity power spectrum with an exponent |α| > 3 indicating that only a few modes are relevant to flow dynamics [3,5,12,13].…”