On the role of pressure in elasto-inertial turbulence

The dynamics of elasto-inertial turbulence is investigated numerically from the perspective of the coupling between polymer dynamics and flow structures. In particular, direct numerical simulations of channel flow with Reynolds numbers ranging from 1000 to 6000 are used to study the formation and dynamics of elastic instabilities and their effects on the flow. Based on the splitting of the pressure into inertial and polymeric contributions, it is shown that the polymeric pressure is a non-negligible component of the total pressure fluctuations, although the rapid inertial part dominates. Unlike Newtonian flows, the slow inertial part is almost negligible in elasto-inertial turbulence. Statistics on the different terms of the Reynolds stress transport equation also illustrate the energy transfers between polymers and turbulence and the redistributive role of pressure. Finally, the trains of cylindrical structures around sheets of high polymer extension that are characteristics of elasto-inertial turbulence are shown to be correlated with the polymeric pressure fluctuations

Exact travelling wave solutions in viscoelastic channel flow

Elasto-inertial turbulence (EIT) is a new, two-dimensional chaotic flow state observed in polymer solutions with possible connections to inertialess elastic turbulence and drag-reduced Newtonian turbulence. In this Letter, we argue that the origins of EIT are fundamentally different from Newtonian turbulence by finding a dynamical connection between EIT and an elasto-inertial linear instability recently found at high Weissenberg numbers (Garg et al. Phys. Rev. Lett. 121, 024502, 2018). This link is established by isolating the first known exact coherent structures in viscoelastic parallel flows - nonlinear elasto-inertial travelling waves (TWs) - borne at the linear instability and tracking them down to substantially lower Weissenberg numbers where EIT exists. These TWs have a distinctive ``arrowhead'' structure in the polymer stretch field and can be clearly recognised, albeit transiently, in EIT, as well as being attractors for EIT dynamics if the Weissenberg number is sufficiently large. Our findings suggest that the dynamical systems picture in which Newtonian turbulence is built around the co-existence of many (unstable) simple invariant solutions populating phase space carries over to EIT, though these solutions rely on elasticity to exist

Polymer Maximum Drag Reduction: A Unique Transitional State

The upper bound of polymer drag reduction is identified as a unique transitional state between laminar and turbulent flow corresponding to the onset of the nonlinear breakdown of flow instabilities

Elasto-inertial turbulence

Turbulence is ubiquitous in nature yet even for the case of ordinary Newtonian fluids like water our understanding of this phenomenon is limited. Many liquids of practical importance however are more complicated (e.g. blood, polymer melts or paints), they exhibit elastic as well as viscous characteristics and the relation between stress and strain is nonlinear. We here demonstrate for a model system of such complex fluids that at high shear rates turbulence is not simply modified as previously believed but it is suppressed and replaced by a new type of disordered motion, elasto-inertial turbulence (EIT). EIT is found to occur at much lower Reynolds numbers than Newtonian turbulence and the dynamical properties differ significantly. In particular the drag is strongly reduced and the observed friction scaling resolves a longstanding puzzle in non-Newtonian fluid mechanics regarding the nature of the so-called maximum drag reduction asymptote. Theoretical considerations imply that EIT will arise in complex fluids if the extensional viscosity is sufficiently large

Multistability of elasto-inertial two-dimensional channel flow

Elasto-inertial turbulence (EIT) is a recently discovered two-dimensional chaotic flow state observed in dilute polymer solutions. It has been hypothesised that the dynamical origins of EIT are linked to a center-mode instability, whose nonlinear evolution leads to a travelling wave with an 'arrowhead' structure in the polymer conformation, a structure also observed instantaneously in simulations of EIT. In this work we conduct a suite of two-dimensional direct numerical simulations spanning a wide range of polymeric flow parameters to examine the possible dynamical connection between the arrowhead and EIT. Our calculations reveal (up to) four co-existent attractors: the laminar state and a steady arrowhead, along with EIT and a 'chaotic arrowhead'. The steady arrowhead is stable for all parameters considered here, while the final pair of (chaotic) flow states are visually very similar and can be distinguished only by the presence of a weak polymer arrowhead structure in the 'chaotic arrowhead' regime. Analysis of energy transfers between the flow and the polymer indicates that both chaotic regimes are maintained by an identical near-wall mechanism and that the weak arrowhead does not play a role. Our results suggest that the arrowhead is a benign flow structure that is disconnected from the self-sustaining mechanics of EIT.Comment: 17 pages, 10 figure

Predicting flow reversals in a computational fluid dynamics simulated thermosyphon using data assimilation

A thermal convection loop is a annular chamber filled with water, heated on the bottom half and cooled on the top half. With sufficiently large forcing of heat, the direction of fluid flow in the loop oscillates chaotically, dynamics analogous to the Earth\u27s weather. As is the case for state-of-the-art weather models, we only observe the statistics over a small region of state space, making prediction difficult. To overcome this challenge, data assimilation (DA) methods, and specifically ensemble methods, use the computational model itself to estimate the uncertainty of the model to optimally combine these observations into an initial condition for predicting the future state. Here, we build and verify four distinct DA methods, and then, we perform a twin model experiment with the computational fluid dynamics simulation of the loop using the Ensemble Transform Kalman Filter (ETKF) to assimilate observations and predict flow reversals. We show that using adaptively shaped localized covariance outperforms static localized covariance with the ETKF, and allows for the use of less observations in predicting flow reversals. We also show that a Dynamic Mode Decomposition (DMD) of the temperature and velocity fields recovers the low dimensional system underlying reversals, finding specific modes which together are predictive of reversal direction

Optimization of over-summer snow storage at midlatitudes and low elevation

Climate change, including warmer winter temperatures, a shortened snowfall season, and more rain-on-snow events, threatens nordic skiing as a sport. In response, oversummer snow storage, attempted primarily using woodchips as a cover material, has been successfully employed as a climate change adaptation strategy by high-elevation and/or high-latitude ski centers in Europe and Canada. Such storage has never been attempted at a site that is both low elevation and midlatitude, and few studies have quantified storage losses repeatedly through the summer. Such data, along with tests of different cover strategies, are prerequisites to optimizing snow storage strategies. Here, we assess the rate at which the volume of two woodchip-covered snow piles (each ∼ 200 m3), emplaced during spring 2018 in Craftsbury, Vermont (45° N and 360 m a.s.l.), changed. We used these data to develop an optimized snow storage strategy. In 2019, we tested that strategy on a much larger, 9300 m3 pile. In 2018, we continually logged air-to-snow temperature gradients under different cover layers including rigid foam, open-cell foam, and woodchips both with and without an underlying insulating blanket and an overlying reflective cover. We also measured ground temperatures to a meter depth adjacent to the snow piles and used a snow tube to measure snow density. During both years, we monitored volume change over the melt season using terrestrial laser scanning every 10- 14 d from spring to fall. In 2018, snow volume loss ranged from 0.29 to 2.81 m3 d-1, with the highest rates in midsummer and lowest rates in the fall; mean rates of volumetric change were 1.24 and 1.50 m3 d-1, 0.55 % to 0.72 % of initial pile volume per day. Snow density did increase over time, but most volume loss was the result of melting. Wet woodchips underlain by an insulating blanket and covered with a reflective sheet were the most effective cover combination for minimizing melt, likely because the aluminized surface reflected incoming short-wave radiation while the wet woodchips provided significant thermal mass, allowing much of the energy absorbed during the day to be lost by long-wave emission at night. The importance of the pile surface-area-tovolume ratio is demonstrated by 4-fold lower rates of volumetric change for the 9300 m3 pile emplaced in 2019; it lost \u3c 0:16 % of its initial volume per day between April and October, retaining ∼ 60 % of the initial snow volume over summer. Together, these data demonstrate the feasibility of oversummer snow storage at midlatitudes and low elevations and suggest efficient cover strategies

DMTs and Covid-19 severity in MS: a pooled analysis from Italy and France

We evaluated the effect of DMTs on Covid-19 severity in patients with MS, with a pooled-analysis of two large cohorts from Italy and France. The association of baseline characteristics and DMTs with Covid-19 severity was assessed by multivariate ordinal-logistic models and pooled by a fixed-effect meta-analysis. 1066 patients with MS from Italy and 721 from France were included. In the multivariate model, anti-CD20 therapies were significantly associated (OR = 2.05, 95%CI = 1.39–3.02, p < 0.001) with Covid-19 severity, whereas interferon indicated a decreased risk (OR = 0.42, 95%CI = 0.18–0.99, p = 0.047). This pooled-analysis confirms an increased risk of severe Covid-19 in patients on anti-CD20 therapies and supports the protective role of interferon