Wall-bounded turbulent shear flows are known to exhibit universal small-scale dynamics that are modulated by large-scale flow structures. Strong pressure gradients complicate this characterization, however. They can cause significant variation of the mean flow in the streamwise direction. For such situations, we perform asymptotic analysis of the Navier–Stokes equations to inform a model for the effect of mean flow growth on near-wall turbulence in a small domain localized to the boundary. The asymptotics are valid whenever the viscous length scale is small relative to the length scale over which the mean flow varies. To ensure the correct momentum environment, a dynamic procedure is introduced that accounts for the additional sources of mean momentum flux through the upper domain boundary arising from the asymptotic terms. Comparisons of the model's low-order, single-point statistics with those from direct numerical simulation and well-resolved large eddy simulation of adverse-pressure-gradient turbulent boundary layers indicate the asymptotic model successfully accounts for the effect of boundary layer growth on the small-scale near-wall turbulence.

Recent experimental and computational studies indicate that near-wall turbulent flows can be characterized by universal small-scale autonomous dynamics that is modulated by large-scale structures. We formulate numerical simulations of near-wall turbulence in a small domain localized to the boundary, whose size scales in viscous units. To mimic the environment in which the near-wall turbulence evolves, the formulation accounts for the flux of mean momentum through the upper boundary of the domain. Comparisons of the model's two-dimensional energy spectra and low-order single-point statistics with the corresponding quantities computed from direct numerical simulations indicate that it successfully captures the dynamics of the small-scale near-wall turbulence.

The transport equations for the variances of the velocity components are investigated using data from direct numerical simulations of incompressible channel flows at friction Reynolds number ($Re_{\unicode[STIX]{x1D70F}}$) up to $Re_{\unicode[STIX]{x1D70F}}=5200$. Each term in the transport equation has been spectrally decomposed to expose the contribution of turbulence at different length scales to the processes governing the flow of energy in the wall-normal direction, in scale and among components. The outer-layer turbulence is dominated by very large-scale streamwise elongated modes, which are consistent with the very large-scale motions (VLSM) that have been observed by many others. The presence of these VLSMs drives many of the characteristics of the turbulent energy flows. Away from the wall, production occurs primarily in these large-scale streamwise-elongated modes in the streamwise velocity, but dissipation occurs nearly isotropically in both velocity components and scale. For this to happen, the energy is transferred from the streamwise-elongated modes to modes with a range of orientations through nonlinear interactions, and then transferred to other velocity components. This allows energy to be transferred more-or-less isotropically from these large scales to the small scales at which dissipation occurs. The VLSMs also transfer energy to the wall region, resulting in a modulation of the autonomous near-wall dynamics and the observed Reynolds number dependence of the near-wall velocity variances. The near-wall energy flows are more complex, but are consistent with the well-known autonomous near-wall dynamics that gives rise to streaks and streamwise vortices. Through the overlap region between outer- and inner-layer turbulence, there is a self-similar structure to the energy flows. The VLSM production occurs at spanwise scales that grow with $y$. There is transport of energy away from the wall over a range of scales that grows with $y$. Moreover, there is transfer of energy to small dissipative scales which grows like $y^{1/4}$, as expected from Kolmogorov scaling. Finally, the small-scale near-wall processes characterised by wavelengths less than 1000 wall units are largely Reynolds number independent, while the larger-scale outer-layer processes are strongly Reynolds number dependent. The interaction between them appears to be relatively simple.

We study the large-scale motions in turbulent plane Couette flows at moderate friction Reynolds number up to $Re_{\unicode[STIX]{x1D70F}}=500$ . Direct numerical simulation (DNS) domains were as large as $100\unicode[STIX]{x03C0}\unicode[STIX]{x1D6FF}\times 2\unicode[STIX]{x1D6FF}\times 5\unicode[STIX]{x03C0}\unicode[STIX]{x1D6FF}$ , where $\unicode[STIX]{x1D6FF}$ is half the distance between the walls. The results indicate that there are streamwise vortices filling the space between the walls that remain correlated over distances in the streamwise direction and that increase strongly with the Reynolds number, so that for the largest Reynolds number studied here, they are correlated across the entire $100\unicode[STIX]{x03C0}\unicode[STIX]{x1D6FF}$ length of the domain. The presence of these very long structures is apparent in the spectra of all three velocity components and the Reynolds stress. In DNS using a smaller domain, the large structures are constrained, eliminating the streamwise variations present in the larger domain. Near the centre of the domain, these large-scale structures contribute as much as half of the Reynolds shear stress.

This paper illustrates one strategy for testing a theory of economic influences on voting. We use a competitive equilibrium model of the economy to determine the impact of an individual's economic position on his or her economic interests and, ultimately, political interests. We then test whether this impact is observed in voting behavior, addressing the resulting specification and estimation problems in the context of U.S. presidential election data. Our empirical results suggest that, despite these formidable problems, we can usefully connect political-economic models and discrete-choice (probit) models of voting.

Preventable diseases not only cause suffering and physical harm, they also impose financial costs on private individuals and public authorities. By disregarding evidence of the safety and effectiveness of vaccines and choosing not to vaccinate their children, some parents are increasing the risk of outbreaks and their attendant costs. In a very real sense, since those families are not currently required to cover the full costs of outbreaks, they are externalizing those costs onto others – individuals affected and society at large. Since non-vaccinating can directly lead to costly outbreaks, this paper argues that it is both fair and desirable to impose those costs upon those making the choice not to vaccinate. There are, in fact, strong policy reasons to support doing so regardless of whether we use an approach based on fault or a no-fault framework. Not only can the decision not to vaccinate be seen as culpable, aside from the culpability consideration, it is appropriate to compel those deciding not to vaccinate to internalize the costs in order to prevent free riding and to mitigate harms to others.

A direct numerical simulation of incompressible channel flow at a friction Reynolds number ( $\mathit{Re}_{{\it\tau}}$ ) of 5186 has been performed, and the flow exhibits a number of the characteristics of high-Reynolds-number wall-bounded turbulent flows. For example, a region where the mean velocity has a logarithmic variation is observed, with von Kármán constant ${\it\kappa}=0.384\pm 0.004$ . There is also a logarithmic dependence of the variance of the spanwise velocity component, though not the streamwise component. A distinct separation of scales exists between the large outer-layer structures and small inner-layer structures. At intermediate distances from the wall, the one-dimensional spectrum of the streamwise velocity fluctuation in both the streamwise and spanwise directions exhibits $k^{-1}$ dependence over a short range in wavenumber $(k)$ . Further, consistent with previous experimental observations, when these spectra are multiplied by $k$ (premultiplied spectra), they have a bimodal structure with local peaks located at wavenumbers on either side of the $k^{-1}$ range.

Political scientists have contributed to the world of electoral systems as scientists and as engineers. Taking stock of recent scientific research, we show that context modifies the effects of electoral rules on political outcomes in specific and systematic ways. We explore how electoral rules shape the inclusion of women and minorities, the depth and nature of political competition, and patterns of redistribution and regulation, and we consider institutional innovations that could promote political equality. Finally, we describe the diverse ways that political scientists produce an impact on the world by sharing and applying their knowledge of the consequences of electoral rules and global trends in reform.