arXiv subjects

Theo A. Lewy

Publications and source records attributed to Theo A. Lewy.

3 recordsLinked to original sources

arXiv2026

Oscillatory shear flows and a new 2D self-sustaining process

A new self-sustaining process (SSP) is identified in an oscillating spatially-homogeneous shear flow using a nonlinear Kelvin mode model. This SSP consists of energetic spanwise-invariant 1D `sheets' and weaker spanwise-dependent 2D fluctuations. It is instantaneously 2D, with a time-dependent invariant direction in the flow-cross-shear plane, and has a varicose symmetry. The sheets oscillate in time and are linearly unstable generating fluctuations which then nonlinearly self-interact to reinforce the sheets. The linear instability of the sheet is shown to be due to a lift-up mechanism acting in tandem with `push-forward', which arises due to the `streamwise' shear of the sheets. As the Reynolds number $Re\rightarrow\infty$, both asymptotics and numerics show SSP lower branches with fluctuation velocity $|\boldsymbol{u}'|\sim Re^{-1/2}$. Implications are discussed for oscillatory wall-bounded flows.

physics.flu-dyn↗

arXiv2026

Localised Arrowheads: The building blocks of elastic turbulence in rectilinear, sheared polymer flows

Pressure-driven flow of a dilute polymer solution has been numerically observed to possess a form of elastic turbulence which is organised around the interactions of localised versions of 2-dimensional `arrowhead' travelling waves (Page et al. Phys. Rev. Lett. 125, 154501, 2020). As a step to confirming this theoretically, we identify spanwise-localised arrowhead travelling waves by tracking a symmetry-breaking bifurcation of the known spanwise-invariant (2D) arrowhead to a spanwise-periodic state and then discovering a secondary modulational instability to a spanwise-localised travelling wave. Spanwise-symmetric and asymmetric localised arrowheads exist with the latter having a phase speed slightly inclined to the streamwise direction. Computations capture the flow randomly switching between spanwise local and global arrowhead states in a streamwise-restricted domain, suggesting they form the building blocks of the chaos. Splitting events are also seen, in which a single localised state spawns multiple arrowheads. However, both cross-shear and spanwise velocities are small suggesting that this elastic turbulence will not be a good mixer.

physics.flu-dyn↗

arXiv2026

Elastic turbulence in highly entangled polymers and wormlike micelles

We show theoretically that an initially homogeneous planar Couette flow of a concentrated polymeric fluid is linearly unstable to the growth of two-dimensional (2D) perturbations, within two widely used constitutive models: the Johnson-Segalman model and the Rolie-Poly model. We perform direct nonlinear simulations of both models in 2D to show that this instability leads to a state of elastic turbulence comprising several narrow shear bands that dynamically coalesce, split and interact. Importantly, we show that this 2D instability arises not only in fluids that have a non-monotonic constitutive curve, and therefore show shear banding in 1D calculations, but also in shear thinning fluids with a monotonic constitutive curve, for which an initially homogeneous base state is stable in 1D. For the former category, the high shear branch of the constitutive curve is unstable to 2D instability in both models, so that the high shear band may be turbulent. In the Rolie-Poly model, the low shear branch is also likewise unstable. Our work provides the first simulation evidence for elastic turbulence in highly entangled polymeric fluids. It also potentially explains rheo-chaotic states seen experimentally in shear banding wormlike micelles. We additionally demonstrate elastic turbulence within both models in the planar Poiseuille geometry.

cond-mat.soft↗