Reynolds-dependence of turbulent skin-friction drag reduction induced by spanwise forcing

This paper examines how increasing the value of the Reynolds number $Re$ affects the ability of spanwise-forcing techniques to yield turbulent skin-friction drag reduction. The considered forcing is based on the streamwise-travelling waves of spanwise wall velocity (Quadrio {\em et al. J. Fluid Mech.}, vol. 627, 2009, pp. 161--178). The study builds upon an extensive drag-reduction database created with Direct Numerical Simulation of a turbulent channel flow for two, 5-fold separated values of $Re$, namely $Re_\tau=200$ and $Re_\tau=1000$. The sheer size of the database, which for the first time systematically addresses the amplitude of the forcing, allows a comprehensive view of the drag-reducing characteristics of the travelling waves, and enables a detailed description of the changes occurring when $Re$ increases. The effect of using a viscous scaling based on the friction velocity of either the non-controlled flow or the drag-reduced flow is described. In analogy with other wall-based drag reduction techniques, like for example riblets, the performance of the travelling waves is well described by a vertical shift of the logarithmic portion of the mean streamwise velocity profile. Except when $Re$ is very low, this shift remains constant with $Re$, at odds with the percentage reduction of the friction coefficient, which is known to present a mild, logarithmic decline. Our new data agree with the available literature, which is however mostly based on low-$Re$ information and hence predicts a quick drop of maximum drag reduction with $Re$. The present study supports a more optimistic scenario, where for an airplane at flight Reynolds numbers a drag reduction of nearly 30\% would still be possible thanks to the travelling waves

Performance losses of drag-reducing spanwise forcing at moderate values of the Reynolds number

A fundamental problem in the field of turbulent skin-friction drag reduction is to determine the performance of the available control techniques at high values of the Reynolds number $Re$. We consider active, predetermined strategies based on spanwise forcing (oscillating wall and streamwise-traveling waves applied to a plane channel flow), and explore via Direct Numerical Simulations (DNS) up to $Re_\tau=2100$ the rate at which their performance deteriorates as $Re$ is increased. To be able to carry out a comprehensive parameter study, we limit the computational cost of the simulations by adjusting the size of the computational domain in the homogeneous directions, compromising between faster computations and the increased need of time-averaging the fluctuating space-mean wall shear-stress. Our results, corroborated by a few full-scale DNS, suggest a scenario where drag reduction degrades with $Re$ at a rate that varies according to the parameters of the wall forcing. In agreement with already available information, keeping them at their low-$Re$ optimal value produces a relatively quick decrease of drag reduction. However, at higher $Re$ the optimal parameters shift towards other regions of the parameter space, and these regions turn out to be much less sensitive to $Re$. Once this shift is accounted for, drag reduction decreases with $Re$ at a markedly slower rate. If the slightly favorable trend of the energy required to create the forcing is considered, a chance emerges for positive net energy savings also at large values of the Reynolds number.Comment: Revised version: change of title, revised intro, small improvements to figures and tex

Non-Hermitian transparency and one-way transport in low-dimensional lattices by an imaginary gauge field

Unidirectional and robust transport is generally observed at the edge of two- or three-dimensional quantum Hall and topological insulator systems. A hallmark of these systems is topological protection, i.e. the existence of propagative edge states that cannot be scattered by imperfections or disorder in the system. A different and less explored form of robust transport arises in non-Hermitian systems in the presence of an {\it imaginary} gauge field. As compared to topologically-protected transport in quantum Hall and topological insulator systems, robust non-Hermitian transport can be observed in {\it lower} dimensional (i.e. one dimensional) systems. In this work the transport properties of one-dimensional tight-binding lattices with an imaginary gauge field are theoretically investigated, and the physical mechanism underlying robust one-way transport is highlighted. Back scattering is here forbidden because reflected waves are evanescent rather than propagative. Remarkably, the spectral transmission of the non-Hermitian lattice is shown to be mapped into the one of the corresponding Hermitian lattice, i.e. without the gauge field, {\it but} computed in the complex plane. In particular, at large values of the gauge field the spectral transmittance becomes equal to one, even in the presence of disorder or lattice imperfections. This phenomenon can be referred to as {\it one-way non-Hermitian transparency}. Robust one-way transport can be also realized in a more realistic setting, namely in heterostructure systems, in which a non-Hermitian disordered lattice is embedded between two homogeneous Hermitian lattices. Such a double heterostructure realizes asymmetric (non-reciprocal) wave transmission. A physical implementation of non-Hermtian transparency, based on light transport in a chain of optical microring resonators, is suggested.Comment: final version, to appear in Physical Review

Robust light transport in non-Hermitian photonic lattices

Combating the effects of disorder on light transport in micro- and nano-integrated photonic devices is of major importance from both fundamental and applied viewpoints. In ordinary waveguides, imperfections and disorder cause unwanted back-reflections, which hinder large-scale optical integration. Topological photonic structures, a new class of optical systems inspired by quantum Hall effect and topological insulators, can realize robust transport via topologically-protected unidirectional edge modes. Such waveguides are realized by the introduction of synthetic gauge fields for photons in a two-dimensional structure, which break time reversal symmetry and enable one-way guiding at the edge of the medium. Here we suggest a different route toward robust transport of light in lower-dimensional (1D) photonic lattices, in which time reversal symmetry is broken because of the {\it non-Hermitian} nature of transport. While a forward propagating mode in the lattice is amplified, the corresponding backward propagating mode is damped, thus resulting in an asymmetric transport that is rather insensitive to disorder or imperfections in the structure. Non-Hermitian transport in two lattice models is considered: a tight-binding lattice with an imaginary gauge field (Hatano-Nelson model), and a non-Hermitian driven binary lattice. In the former case transport in spite of disorder is ensured by a mobility edge that arises because of a non-Hermitian delocalization transition. The possibility to observe non-Hermitian delocalization induced by a synthetic 'imaginary' gauge field is suggested using an engineered coupled-resonator optical waveguide (CROW) structure.Comment: revised and extended version, to appear in Sci. Re

The Wall-Jet Region of a Turbulent Jet Impinging on Smooth and Rough Plates

The study reports direct numerical simulations of a turbulent jet impinging onto smooth and rough surfaces at Reynolds number Re = 10,000 (based on the jet mean bulk velocity and diameter). Surface roughness is included in the simulations using an immersed boundary method. The deflection of the flow after jet impingement generates a radial wall-jet that develops parallel to the mean plate surface. The wall-jet is structured into an inner and an outer layer that, in the limit of infinite local Reynolds number, resemble a turbulent boundary layer and a free-shear flow. The investigation assesses the self-similar character of the mean radial velocity and Reynolds stresses profiles scaled by inner and outer layer units for varying size of the roughness topography. Namely the usual viscous units $u_{\tau}$ and $\delta_{\upsilon}$ are used as inner layer scales, while the maximum radial velocity $u_{m}$ and its wall-normal location $z_{m}$ are used as outer layer scales. It is shown that the self-similarity of the mean radial velocity profiles scaled by outer layer units is marginally affected by the span of roughness topographies investigated, as outer layer velocity and length reference scales do not show a significantly modified behavior when surface roughness is considered. On the other hand, the mean radial velocity profiles scaled by inner layer units show a considerable scatter, as the roughness sub-layer determined by the considered roughness topographies extends up to the outer layer of the wall-jet. Nevertheless, the similar character of the velocity profiles appears to be conserved despite the profound impact of surface roughness

Rehabilitation that incorporates virtual reality is more effective than standard rehabilitation for improving walking speed, balance and mobility after stroke: a systematic review

Abstract Question: In people after stroke, does virtual reality based rehabilitation (VRBR) improve walking speed, balance and mobility more than the same duration of standard rehabilitation? In people after stroke, does adding extra VRBR to standard rehabilitation improve the effects on gait, balance and mobility? Design: Systematic review with meta-analysis of randomised trials. Participants: Adults with a clinical diagnosis of stroke. Intervention: Eligible trials had to include one these comparisons: VRBR replacing some or all of standard rehabilitation or VRBR used as extra rehabilitation time added to a standard rehabilitation regimen. Outcome measures: Walking speed, balance, mobility and adverse events. Results: In total, 15 trials involving 341 participants were included. When VRBR replaced some or all of the standard rehabilitation, there were statistically significant benefits in walking speed (MD 0.15 m/s, 95% CI 0.10 to 0.19), balance (MD 2.1 points on the Berg Balance Scale, 95% CI 1.8 to 2.5) and mobility (MD 2.3 seconds on the Timed Up and Go test, 95% CI 1.2 to 3.4). When VRBR was added to standard rehabilitation, mobility showed a significant benefit (0.7 seconds on the Timed Up and Go test, 95% CI 0.4 to 1.1), but insufficient evidence was found to comment about walking speed (one trial) and balance (high heterogeneity). Conclusion: Substituting some or all of a standard rehabilitation regimen with VRBR elicits greater benefits in walking speed, balance and mobility in people with stroke. Although the benefits are small, the extra cost of applying virtual reality to standard rehabilitation is also small, especially when spread over many patients in a clinic. Adding extra VRBR time to standard rehabilitation also has some benefits; further research is needed to determine if these benefits are clinically worthwhile. [Corbetta D, Imeri F, Gatti R (2015) Rehabilitation that incorporates virtual reality is more effective than standard rehabilitation for improving walking speed, balance and mobility after stroke: a systematic review. Journal of Physiotherapy 61: 117–124

Global energy budgets in turbulent Couette and Poiseuille flows

Turbulent plane Poiseuille and Couette flows share the same geometry, but produce their flow rate owing to different external drivers: pressure gradient and shear, respectively. By looking at integral energy fluxes, we pose and answer the question as to which flow performs better at creating flow rate. We define a flow efficiency, which quantifies the fraction of power used to produce flow rate instead of being wasted as a turbulent overhead; effectiveness, instead, describes the amount of flow rate produced by a given power. The work by Gatti et al. (J. Fluid Mech., vol. 857, 2018, pp. 345–373), where the constant power input concept was developed to compare turbulent Poiseuille flows with drag reduction, is here extended to compare different flows. By decomposing the mean velocity field into a laminar contribution and a deviation, analytical expressions are derived which are the energy-flux equivalents of the FIK identity. These concepts are applied to literature data supplemented by a new set of direct numerical simulations, to find that Couette flows are less efficient but more effective than Poiseuille flows. The reason is traced to the more effective laminar component of Couette flows, which compensates for their higher turbulent activity. It is also observed that, when the fluctuating fields of the two flows are fed with the same total power fraction, Couette flows dissipate a smaller percentage of it via turbulent dissipation. A decomposition of the fluctuating field into large and small scales explains this feature: Couette flows develop stronger large-scale structures, which alter the mean flow while contributing less significantly to dissipation