Tonal noise emitted from the trailing edge of an airfoil is considered using modal analysis techniques to investigate secondary quadrupole tones. We examine the origin of quadrupole sound generated from two-dimensional unsteady laminar flow over a NACA0012 airfoil. In this paper, we consider two flow configurations at Mach numbers of $M_\infty = 0.1$ and 0.05 that lead to different acoustic characteristics: the former has a significant high-frequency quadrupole noise source, whereas the latter does not. We use vortex sound theory, dynamic mode decomposition (DMD), and resolvent analysis to analyze the sound source. First, we employ DMD modes to reveal that the quadrupole sound is only observed in the higher Mach number case. Next, the vortex dynamics in the vicinity of the trailing edge are studied to identify the origin of quadrupole sound. It is found that the quadrupole sound is caused by vortex shedding in the vicinity of the trailing edge. The complex vortex interaction between both sides of the airfoil strengthens the quadrupole source in the higher Mach number case, while it is negligible in the lower one. Furthermore, we perform resolvent analysis to examine the vortex generation over the airfoil. The resolvent mode indicates that the interaction between the vortices on both sides of the airfoil causes a multi-scale vortex structure on the suction-side wall.

Through triglobal resolvent analysis, we reveal the effects of wing tip and sweep angle on laminar separated wakes over swept wings. For the present study, we consider wings with semi-aspect ratios from $1$ to $4$, sweep angles from $0^\circ$ to $45^\circ$ and angles of attack of $20^\circ$ and $30^\circ$ at a chord-based Reynolds number of $400$ and a Mach number of $0.1$. Using direct numerical simulations, we observe that unswept wings develop vortex shedding near the wing root with a quasi-steady tip vortex. For swept wings, vortex shedding is seen near the wing tip for low sweep angles, while the wakes are steady for wings with high sweep angles. To gain further insights into the mechanisms of flow unsteadiness, triglobal resolvent analysis is used to identify the optimal spatial input–output mode pairs and the associated gains over a range of frequencies. The three-dimensional forcing and response modes reveal that harmonic fluctuations are directed towards the root for unswept wings and towards the wing tip for swept wings. The overlapping region of the forcing–response mode pairs uncovers triglobal resolvent wavemakers associated with self-sustained unsteady wakes of swept wings. Furthermore, we show that for low-aspect-ratio wings optimal perturbations develop globally over the entire wingspan. The present study uncovers physical insights on the effects of tip and sweep on the growth of optimal harmonic perturbations and the wake dynamics of separated flows over swept wings.

We reveal the effects of sweep on the wake dynamics around NACA 0015 wings at high angles of attack using direct numerical simulations and resolvent analysis. The influence of sweep on the wake dynamics is considered for sweep angles from $0^\circ$ to $45^\circ$ and angles of attack from $16^\circ$ to $30^\circ$ for a spanwise periodic wing at a chord-based Reynolds number of $400$ and a Mach number of $0.1$. Wing sweep affects the wake dynamics, especially in terms of stability and spanwise fluctuations with implications on the development of three-dimensional (3-D) wakes. We observe that wing sweep attenuates spanwise fluctuations. Even as the sweep angle influences the wake, force and pressure coefficients can be collapsed for low angles of attack when examined in wall-normal and wingspan-normal independent flow components. Some small deviations at high sweep and incidence angles are attributed to vortical wake structures that impose secondary aerodynamic loads, revealed through the force element analysis. Furthermore, we conduct global resolvent analysis to uncover oblique modes with high disturbance amplification. The resolvent analysis also reveals the presence of wavemakers in the shear-dominated region associated with the emergence of 3-D wakes at high angles of attack. For flows at high sweep angles, the optimal convection speed of the response modes is shown to be faster than the optimal wavemakers speed suggesting a mechanism for the attenuation of perturbations. The present findings serve as a fundamental stepping stone to understanding separated flows at higher Reynolds numbers.

We consider the use of sparsity-promoting norms in obtaining localised forcing structures from resolvent analysis. By formulating the optimal forcing problem as a Riemannian optimisation, we are able to maximise cost functionals whilst maintaining a unit-energy forcing. Taking the cost functional to be the energy norm of the driven response results in a traditional resolvent analysis and is solvable by a singular value decomposition (SVD). By modifying this cost functional with the $L_1$-norm, we target spatially localised structures that provide an efficient amplification in the energy of the response. We showcase this optimisation procedure on two flows: plane Poiseuille flow at Reynolds number $Re=4000$, and turbulent flow past a NACA 0012 aerofoil at $Re=23\,000$. In both cases, the optimisation yields sparse forcing modes that maintain important features of the structures arising from an SVD in order to provide a gain in energy. These results showcase the benefits of utilising a sparsity-promoting resolvent formulation to uncover sparse forcings, specifically with a view to using them as actuation locations for flow control.

This research examines whether an alternative exchange rate policy could have mitigated Germany’s recession from April 1930 to May 1932, when Heinrich Brüning was Reichskanzler of the Weimar Republic. Using an open-economy dynamic model as our analytical framework, we examine the arguments against adopting the devaluation policy. Our counterfactual analysis suggests that a widely held belief—that floating the Reichsmark would have led to high inflation—is unwarranted. Despite Germany’s high foreign debt, floating the Reichsmark would have led to less of a decline in both real GDP and employment for the country during the Great Depression.

We use resolvent analysis to develop a physics-based, open-loop, unsteady control strategy to attenuate pressure fluctuations in turbulent flow over a rectangular cavity with a length-to-depth ratio of $6$ at a Mach number of $1.4$ and a Reynolds number based on cavity depth of $10\,000$. Large-eddy simulations (LES) of the baseline uncontrolled flow reveal the dominance of Rossiter modes II and IV that generate high-amplitude unsteadiness via trailing-edge impingement and oblique shock waves that obstruct the free stream. To suppress the oscillations, we introduce three-dimensional unsteady blowing along the cavity leading edge. We leverage resolvent analysis as a linear model with respect to the baseline flow to guide the selections of the optimal spanwise wavenumber and frequency of the unsteady actuation input for a fixed momentum coefficient of 0.02. Instead of choosing the most amplified resolvent forcing modes, we seek a disturbance that yields sustained amplification of the primary response mode-based kinetic energy distribution over the entire cavity length. This necessary but not sufficient guideline for effective mean flow modification is evaluated using LES of the controlled cavity flows. The most effective control case reduces the pressure root mean square level up to $52\,\%$ along cavity walls relative to the baseline and is approximately twice that achievable by comparable steady blowing. Dynamic mode decomposition on the controlled flows confirms that the optimal actuation input indeed suppresses the formation of the large-scale Rossiter modes. It is expected that the present flow control guideline derived from resolvent analysis will also be applicable at higher Reynolds numbers with the aid of physical insights and further validation.

We present a network-based modal analysis technique that identifies key dynamical paths along which perturbations amplify over a time-varying base flow. This analysis is built upon the Katz centrality, which reveals the flow structures that can effectively spread perturbations over a time-evolving network of vortical interactions on the base flow. Motivated by the resolvent form of the Katz function, we take the singular value decomposition of the resulting communicability matrix, complementing the resolvent analysis for fluid flows. The right-singular vectors, referred to as the broadcast modes, give insights into the sensitive regions where introduced perturbations can be effectively spread and amplified over the entire fluid-flow network that evolves in time. We apply this analysis to a two-dimensional decaying isotropic turbulence. The broadcast mode reveals that vortex dipoles are important structures in spreading perturbations. By perturbing the flow with the principal broadcast mode, we demonstrate the utility of the insights gained from the present analysis for effectively modifying the evolution of turbulent flows. The current network-inspired work presents a novel use of network analysis to guide flow control efforts, in particular for time-varying base flows.

Resolvent analysis is performed to identify the origin of two-dimensional transonic buffet over an airfoil. The base flow for the resolvent analysis is the time-averaged flow over a NACA 0012 airfoil at a chord-based Reynolds number of 2000 and a free-stream Mach number of 0.85. We reveal that the mechanism of buffet is buried underneath the global low-Reynolds-number flow physics. At this low Reynolds number, the dominant flow feature is the von Kármán shedding. However, we show that with the appropriate forcing input, buffet can appear even at a Reynolds number that is much lower than what is traditionally associated with transonic buffet. The source of buffet is identified to be at the shock foot from the windowed resolvent analysis, which is validated by companion simulations using sustained forcing inputs based on resolvent modes. We also comment on the role of perturbations in the vicinity of the trailing edge. The present study not only provides insights on the origin of buffet but also serves a building block for low-Reynolds-number compressible aerodynamics in light of the growing interests in Martian flights.

We propose a cluster-based control strategy for feedback control of post-stall separated flows over an airfoil. The present approach partitions the flow trajectories (force measurements) into clusters, which correspond to characteristic coarse-grained phases in a low-dimensional feature space. A feedback control law (using blowing/suction actuation) is then sought for each cluster state through iterative evaluation and downhill simplex search to minimize power consumption in aerodynamic flight. The optimized control laws re-route the flow trajectories to the aerodynamically favourable regions in the feature space in a model-free manner. Utilizing a limited number of sensor measurements for both clustering and optimization, these feedback laws were determined in only $O(10)$ iterations. The objective of the present work is not necessarily to suppress flow separation but to minimize the desired cost function to achieve enhanced aerodynamic performance. The present approach is applied to the control of two- and three-dimensional separated flows over a NACA 0012 airfoil in large-eddy simulations at an angle of attack of $9^{\circ }$, Reynolds number $Re=23\,000$ and free-stream Mach number $M_{\infty }=0.3$. The optimized control laws avoid the intermittent occurrence of long-period shedding associated with high-drag clusters, thus lowering the mean drag. The present work aims to address some of the challenges associated with feedback control design for turbulent separated flows at moderate Reynolds number.

We use resolvent analysis to design active control techniques for separated flows over a NACA 0012 airfoil. Spanwise-periodic flows over the airfoil at a chord-based Reynolds number of $23\,000$ and a free-stream Mach number of $0.3$ are considered at two post-stall angles of attack of $6^{\circ }$ and $9^{\circ }$. Near the leading edge, localized unsteady thermal actuation is introduced in an open-loop manner with two tunable parameters of actuation frequency and spanwise wavelength. To provide physics-based guidance for the effective choice of these control input parameters, we conduct global resolvent analysis on the baseline turbulent mean flows to identify the actuation frequency and wavenumber that provide large perturbation energy amplification. The present analysis also considers the use of a temporal filter to limit the time horizon for assessing the energy amplification to extend resolvent analysis to unstable base flows. We incorporate the amplification and response mode from resolvent analysis to provide a metric that quantifies momentum mixing associated with the modal structure. This metric is compared to the results from a large number of three-dimensional large-eddy simulations of open-loop controlled flows. With the agreement between the resolvent-based metric and the enhancement of aerodynamic performance found through large-eddy simulations, we demonstrate that resolvent analysis can predict the effective range of actuation frequency as well as the global response to the actuation input. We believe that the present resolvent-based approach provides a promising path towards mean flow modification by capitalizing on the dominant modal mixing.

In this paper, we make the case that an argument for price-level targeting over inflation targeting need not to be based on some overly restrictive assumptions. We adopt a theoretical framework that deviates from the assumption of rational expectation, and that takes into account the cognitive limitations and a “trial and error” learning mechanism of the agents. The (im)perfect credibility of various monetary policies (e.g., a Taylor-type rule, strict domestic inflation targeting, strict consumer price index (CPI) inflation targeting, exchange rate peg, and domestic price-level and CPI-level targeting) may lead agents to react according to their expectation rules, and then create various degrees of booms and busts in output and inflation. Therefore, relaxing the rational expectation hypothesis has potential consequences for policy planning. We find that price-level targeting prevails over inflation targeting even under different expectation formation and even when the announced inflation target is not fully credible. The counterfactual analysis and sensitivity test confirm that CPI-level targeting is the most effective for improving social welfare and stability in an open economy. The business cycles induced by animal spirits are enhanced by strict inflation targeting.

The application of local periodic heating for control of a spatially developing shear layer downstream of a finite-thickness splitter plate is examined by numerically solving the two-dimensional Navier–Stokes equations. At the trailing edge of the plate, an oscillatory heat flux boundary condition is prescribed as the thermal forcing input to the shear layer. The thermal forcing introduces a low level of oscillatory surface vorticity flux and baroclinic vorticity at the actuation frequency in the vicinity of the trailing edge. The vortical perturbations produced can independently excite the fundamental instability that accounts for shear layer roll-up as well as the subharmonic instability that encourages the vortex pairing process farther downstream. We demonstrate that the nonlinear dynamics of a spatially developing shear layer can be modified by local oscillatory heat flux as a control input. We believe that this study provides a basic foundation for flow control using thermal-energy-deposition-based actuators such as thermophones and plasma actuators.

Background: Executive dysfunction is not uncommon in patients with amnestic mild cognitive impairment (aMCI). This study aimed to investigate the applicability of executive function tests (EFTs) in aMCI as an aid in establishing the diagnosis of multi-domain MCI.

Methods: One hundred and twenty (120) aMCI patients, 126 Alzheimer's disease (AD) patients, and 100 normal controls were enrolled. The EFTs evaluated included the trail making test, digit backward span, Stroop color–word test, and design fluency and category fluency tests.

Results: Of the aMCI participants, 66% exhibited impairment in at least one EFT. Among the five selected EFTs, the category fluency test was the most discriminative in detecting executive dysfunction between patients with aMCI (standardized β = 0.264) or AD (standardized β = 0.361) with the controls, followed by the Stroop test. The performance of aMCI patients with two or more impaired EFTs was significantly different from those of controls but not from those of AD patients.

Conclusion: In the clinical setting, aMCI patients who fail in two or more EFTs may represent a unique population with multi-domain MCI that require close follow-up.

Blue marlin are sexually dimorphic in size-at-age and other biological characteristics. However, few studies have examined the possible impact of sexual dimorphism on the population parameters and the ratios of fishing to total mortality (the exploitation ratios) for this species. We analyzed sex-specific catch-at-length data for blue marlin collected from the Taiwanese tuna longline fishery in the northwest Pacific Ocean, ranging between 100–311 cm in eye to fork length (EFL) for females and 100–236 cm EFL for males, and show that the proportion of females in the catch (the sex ratio) increases with length, with females reaching larger body sizes than males. Minor differences in fishery sex ratios among months were observed. Growth parameters, length structures, and natural mortality rates were estimated to differ between males and females, while fishing mortality rates were found to be similar. Nevertheless, the exploitation ratio for females was higher than that for males. We suggest that growth parameters and natural mortality rates should be sex-specific when assessments for sexually-dimorphic species such as blue marlin are conducted, and that management of blue marlin fisheries could be developed based on size limit regulations for large individuals.

All suicides (n=12 497) in Taiwan in 2001–2004 were identified from mortality records retrieved from the National Health Insurance Database. Altogether, 95.1% of females and 84.9% of males had been in contact with healthcare services in the year before their death. Females received significantly more diagnoses of psychiatric disorders (48.0% v. 30.2%) and major depression (17.8% v. 7.4%) than males. Such differences were consistent across different medical settings where contact with hospital-based non-psychiatric physicians was as common as with general practitioners (GPs). However, diagnoses of psychiatric disorders were underdiagnosed in both genders.