A tale of two airfoils: resolvent-based modelling of an oscillator vs. an amplifier from an experimental mean

The flows around a NACA 0018 airfoil at a Reynolds number of 10250 and angles of attack of alpha = 0 (A0) and alpha = 10 (A10) are modelled using resolvent analysis and limited experimental measurements obtained from particle image velocimetry. The experimental mean velocity profiles are data-assimilated so that they are solutions of the incompressible Reynolds-averaged Navier-Stokes equations forced by Reynolds stress terms which are derived from experimental data. Spectral proper orthogonal decompositions (SPOD) of the velocity fluctuations and nonlinear forcing find low-rank behaviour at the shedding frequency and its higher harmonics for the A0 case. In the A10 case, low-rank behaviour is observed for the velocity fluctuations in two bands of frequencies. Resolvent analysis of the data-assimilated means identifies low-rank behaviour only in the vicinity of the shedding frequency for A0 and none of its harmonics. The resolvent operator for the A10 case, on the other hand, identifies two linear mechanisms whose frequencies are a close match with those identified by SPOD. It is also shown that the second linear mechanism, corresponding to the Kelvin-Helmholtz instability in the shear layer, cannot be identified just by considering the time-averaged experimental measurements as a mean flow due to the fact that experimental data are missing near the leading edge. The A0 case is classified as an oscillator where the flow is organised around an intrinsic instability while the A10 case behaves like an amplifier whose forcing is unstructured. For both cases, resolvent modes resemble those from SPOD when the operator is low-rank. To model the higher harmonics where this is not the case, we add parasitic resolvent modes, as opposed to classical resolvent modes which are the most amplified, by approximating the nonlinear forcing from limited triadic interactions of known resolvent modes.Comment: 32 pages, 23 figure

Influence of a local change of depth on the behavior of bouncing oil drops

The work of Couder \textit{et al} (see also Bush \textit{et al}) inspired consideration of the impact of a submerged obstacle, providing a local change of depth, on the behavior of oil drops in the bouncing regime. In the linked videos, we recreate some of their results for a drop bouncing on a uniform depth bath of the same liquid undergoing vertical oscillations just below the conditions for Faraday instability, and show a range of new behaviors associated with change of depth. This article accompanies a fluid dynamics video entered into the Gallery of Fluid Motion of the 66th Annual Meeting of the APS Division of Fluid Dynamics.Comment: High and low resolutions videos included as ancillary file

On non-normality and classification of amplification mechanisms in stability and resolvent analysis

We seek to quantify non-normality of the most amplified resolvent modes and predict their features based on the characteristics of the base or mean velocity profile. A 2-by-2 model linear Navier-Stokes (LNS) operator illustrates how non-normality from mean shear distributes perturbation energy in different velocity components of the forcing and response modes. The inverse of their inner product, which is unity for a purely normal mechanism, is proposed as a measure to quantify non-normality. In flows where there is downstream spatial dependence of the base/mean, mean flow advection separates the spatial support of forcing and response modes which impacts the inner product. Success of mean stability analysis depends on the normality of amplification. If the amplification is normal, the resolvent operator written in its dyadic representation reveals that the adjoint and forward stability modes are proportional to the forcing and response resolvent modes. If the amplification is non-normal, then resolvent analysis is required to understand the origin of observed flow structures. Eigenspectra and pseudospectra are used to characterize these phenomena. Two test cases are studied: low Reynolds number cylinder flow and turbulent channel flow. The first deals mainly with normal mechanisms and quantification of non-normality using the inverse inner product of the leading forcing and response modes agrees well with the product of the resolvent norm and distance between the imaginary axis and least stable eigenvalue. In turbulent channel flow, structures result from both normal and non-normal mechanisms. Mean shear is exploited most efficiently by stationary disturbances while bounds on the pseudospectra illustrate how non-normality is responsible for the most amplified disturbances at spatial wavenumbers and temporal frequencies corresponding to well-known turbulent structures

Reconstruction and Estimation of Flows Using Resolvent Analysis and Data-Assimilation

A flow reconstruction methodology is presented for incompressible, statistically stationary flows using resolvent analysis and data-assimilation. The only inputs necessary for the procedure are a rough approximation of the mean profile and a single time-resolved measurement. The objective is to estimate both the mean and fluctuating states of experimental flows with limited measurements which do not include pressure. The input data may be incomplete, in the sense that measurements near a body are difficult to obtain with techniques such as particle image velocimetry (PIV), or contaminated by noise. The tools developed in this thesis are capable of filling in missing data and reducing the amount of measurement noise by leveraging the governing equations. The reconstructed flow is capable of estimating fluctuations where time-resolved data are not available and solving the flow on larger domains where the mean profile is not known. The first part of the thesis focuses on how resolvent analysis of the mean flow selects amplification mechanisms. Eigenspectra and pseudospectra of the mean linear Navier-Stokes (LNS) operator are used to characterize amplification mechanisms in flows where linear mechanisms are important. The real parts of the eigenvalues are responsible for resonant amplification and the resolvent operator is low-rank when the eigenvalues are sufficiently separated in the spectrum. Two test cases are studied: low Reynolds number cylinder flow and turbulent channel flow. The latter is studied by considering well-known turbulent structures while the former contains a marginally stable eigenvalue which drowns out the effect of other eigenvalues over a large range of temporal frequencies. There is a geometric manifestation of this dominant mode in the mean profile, suggesting that it leaves a significant footprint on the time-averaged flow that the resolvent can identify. The resolvent does not provide an efficient basis at temporal frequencies where there is no separation of singular values. It can still be leveraged, nevertheless, to identify coherent structures in the flow by approximating the nonlinear forcing from the interaction of highly amplified coherent structures. The second part of the thesis extends the framework of Foures et al. (2014), who data-assimilated the mean cylinder wake at very low Reynolds numbers. The contributions presented here are to assess the minimum domain for successfully reconstructing Reynolds stress gradients, modifying the algorithm to assimilate mean pressure, determining whether weighting input measurements contributes to improved performance, and adapting the method to experimental data at higher Reynolds numbers. The results from data-assimilating the mean cylinder wake at low Reynolds numbers suggest that the measurement domain needs to coincide with the spatial support of the Reynolds stress gradients while point weighting has a minimal impact on the performance. Finally, a smoothing procedure adapted from Foures et al. (2014) is proposed to cope with data-assimilating an experimental mean profile obtained from PIV data. The data-assimilated mean profiles for an idealized airfoil and NACA 0018 airfoil are solved on a large domain making the mean profile suitable for global resolvent analysis. Data-assimilation is also able to fill in missing or unreliable vectors near the airfoil surface. The final piece of the thesis is to synthesize the knowledge and techniques developed in the first two parts to reconstruct the experimental flow around a NACA 0018 airfoil. Preliminary results are presented for the case where α = 0° and Re = 10250. The mean profile is data-assimilated and used as an input to resolvent analysis to educe coherent structures in the flow. The resolvent operator for non- amplified temporal frequencies is forced by an approximated nonlinear forcing. The amplitude and phase of the modes are obtained from the discrete Fourier-transform of a time-resolved probe point measurement. The final reconstruction contains less measurement noise compared to the PIV snapshots and obeys the incompressible Navier-Stokes equations (NSE). The thesis concludes with a discussion of how elements of this methodology can be incorporated into the development of estimators for turbulent flows at high Reynolds numbers.</p

Water impacting on superhydrophobic macrotextures

International audienceIt has been recently shown that the presence of macrotextures on superhydrophobic materials can markedly modify the dynamics of water impacting them, and in particular significantly reduce the contact time of bouncing drops, compared with what is observed on a flat surface. This finding constitutes a significant step in the maximization of water repellency, since it enables to minimize even further the contact between solid and liquid. It also opens a new axis of research on the design of super-structures to induce specific functions such as anti-freezing, liquid fragmentation and/or recomposition, guiding, trapping and so on. Here we show that the contact time of drops bouncing on a repellent macrotexture takes discrete values when varying the impact speed. This allows us to propose a quantitative analysis of the reduction of contact time and thus to understand how and why macrotextures can control the dynamical properties of bouncing drops

Role of parasitic modes in nonlinear closure via the resolvent feedback loop

We use the feedback formulation of McKeon and Sharma [J. Fluid Mech. 658, 336 (2010)], where the nonlinear term in the Navier-Stokes equations is treated as an intrinsic forcing of the linear resolvent operator, to educe the structure of fluctuations in the range of scales (wave numbers) where linear mechanisms are not active. In this region, the absence of dominant linear mechanisms is reflected in the lack of low-rank characteristics of the resolvent and in the disagreement between the structure of resolvent modes and actual flow features. To demonstrate the procedure, we choose low Reynolds number cylinder flow and the Couette equilibrium solution EQ1, which are representative of very low-rank flows dominated by one linear mechanism. The former is evolving in time, allowing us to compare resolvent modes with dynamic mode decomposition (DMD) modes at the first and second harmonics of the shedding frequency. There is a match between the modes at the first harmonic but not at the second harmonic where there is no separation of the resolvent operator's singular values. We compute the self-interaction of the resolvent mode at the shedding frequency and illustrate its similarity to the nonlinear forcing of the second harmonic. When it is run through the resolvent operator, the “forced” resolvent mode shows better agreement with the DMD mode. A similar phenomenon is observed for the fundamental streamwise wave number of the EQ1 solution and its second harmonic. The importance of parasitic modes, labeled as such since they are driven by the amplified frequencies, is their contribution to the nonlinear forcing of the main amplification mechanisms as shown for the shedding mode, which has subtle discrepancies with its DMD counterpart

Genetic mechanisms of critical illness in COVID-19.

Host-mediated lung inflammation is present1, and drives mortality2, in the critical illness caused by coronavirus disease 2019 (COVID-19). Host genetic variants associated with critical illness may identify mechanistic targets for therapeutic development3. Here we report the results of the GenOMICC (Genetics Of Mortality In Critical Care) genome-wide association study in 2,244 critically ill patients with COVID-19 from 208 UK intensive care units. We have identified and replicated the following new genome-wide significant associations: on chromosome 12q24.13 (rs10735079, P = 1.65 × 10-8) in a gene cluster that encodes antiviral restriction enzyme activators (OAS1, OAS2 and OAS3); on chromosome 19p13.2 (rs74956615, P = 2.3 × 10-8) near the gene that encodes tyrosine kinase 2 (TYK2); on chromosome 19p13.3 (rs2109069, P = 3.98 ×  10-12) within the gene that encodes dipeptidyl peptidase 9 (DPP9); and on chromosome 21q22.1 (rs2236757, P = 4.99 × 10-8) in the interferon receptor gene IFNAR2. We identified potential targets for repurposing of licensed medications: using Mendelian randomization, we found evidence that low expression of IFNAR2, or high expression of TYK2, are associated with life-threatening disease; and transcriptome-wide association in lung tissue revealed that high expression of the monocyte-macrophage chemotactic receptor CCR2 is associated with severe COVID-19. Our results identify robust genetic signals relating to key host antiviral defence mechanisms and mediators of inflammatory organ damage in COVID-19. Both mechanisms may be amenable to targeted treatment with existing drugs. However, large-scale randomized clinical trials will be essential before any change to clinical practice