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Wall turbulence consists of various sizes of vortical structures that induce flow circulation around a wide range of closed Eulerian loops. Here we investigate the multiscale properties of circulation around such loops in statistically homogeneous planes parallel to the wall. Using a high-resolution direct numerical simulation database of turbulent channels at Reynolds numbers of $Re_τ=180$, 550, 1000 and 5200, circulation statistics are obtained in planes at different wall-normal heights. Intermittency of circulation in the planes of the outer flow ($y^+ \gtrsim 0.1Re_τ$) takes the form of universal bifractality as in homogeneous and isotropic turbulence. The bifractal character simplifies to space-filling character close to the wall, with scaling exponents that are linear in the moment order, and lower than those given by the Kolmogorov paradigm. The probability density functions of circulation are long-tailed in the outer bifractal region, {with evidence showing their invariance with respect to the loop aspect ratio}, while those in the inner region are closely Gaussian. The unifractality near the wall implies that the circulation there is not intermittent in character.

The velocity statistics reveal non-universality in both three-dimensional (3-D) and two-dimensional (2-D) turbulence, despite both prototype systems containing an energy inertial range with constant energy flux. Recently, statistics of scale-dependent velocity circulation exhibit universal bifractal behavior in 2-D and 3-D hydrodynamic turbulence and quantum turbulence, where the circulation scale is defined as the square root of the minimum area enclosed by the loop. This loop-shape independent definition of scale bases on the area rule of circulation first proposed by Migdal: the probability density function (PDF) of circulation is only a function of the minimal surface area enclosed by the loop but not the shape of the loop. This paper demonstrates that the derivation of the circulation area rule can be generalized to all scales in 2-D instability-driven turbulence, not limited to the inertial range. However, the area rule is not the only solution to the loop equation, so it may not be observed. Another necessary condition for the validity of the area rule is that the second-order momentum of circulation is loop-shape independent. By deriving the relationship between the second-

We put forward a novel formulation of the vortex gas model of turbulent circulation statistics to address the challenging case of nonplanar circulation contours. Relying upon a field-theoretical description, statistical moments of the circulation turn out to be functionally dependent on specific {\it{optimal surfaces}} bounded by the circulation loops. Circulation is modeled in the optimal curved spaces with the help of scalar vertex operators that represent the multifractal density fluctuations of Gaussian-correlated vortex structures. We show that minimal surfaces are optimal within the inertial range, but subdominant deviations are expected to become significant for contours with linear dimensions close to the Kolmogorov dissipation length. As a case study, we demonstrate the model's applicability through a Monte Carlo evaluation of the circulation probability distribution function for a nonplanar contour, which is in excellent agreement with results of extensive direct numerical simulations.

The data circulation is a complex scenario involving a large number of participants and different types of requirements, which not only has to comply with the laws and regulations, but also faces multiple challenges in technical and business areas. In order to systematically and comprehensively address these issues, it is essential to have a comprehensive and profound understanding of 'data circulation'. The traditional analysis method tends to proceed based on the traditional circulation model of commodities, that is, tangible objects, which has some defects and shortcomings, and tends to be a formalized approach, which is faced numerous challenges in practice. This paper analyzes the circulation of data with a philosophical approach, obtains the new explication of data and executing entity, and provides a new definition of the concepts of data utilization and data key stakeholders (objects). At the same time, it puts forward the idea of ``data alienation'', and constructs a new interpretive framework of ``data circulation''. Based on the framework of this interpretation, it is clearly proposed that ``data alienation'' is the core of ``data circulation'', benefit distribution is t

Chiral quantum state circulation is the unidirectional transfer of a quantum state from one subsystem to the next. It is essential to the working of a quantum computer; for instance, for state preparation and isolation. We propose a cavity-QED architecture consisting of three cavities coupled to a qubit, in which \emph{any} photonic state of cavity 1 with sufficiently many photons circulates to cavity 2 after a fixed time interval, and then to cavity 3 and back to 1. Cavity-state circulation arises from topologically protected chiral boundary states in the associated photon lattice and is thus robust to perturbation. We compute the circulation period in the semi-classical limit, demonstrate that circulation persists for time-scales diverging with the total photon number, and provide a Floquet protocol to engineer the desired Hamiltonian. Superconducting qubits offer an ideal platform to build and test these devices in the near term.

We study experimentally the statistical properties and evolution of circulation in a turbulent flow passing through a smooth 2-D contraction. The turbulence is generated with an active grids to reach $Re_λ \simeq 220$ at the inlet to the 2.5:1 contraction. We employ time-resolved 3-D Lagrangian Particle Tracking technique with the Shake-The-Box algorithm to obtain volumetric velocity fields which we use to calculate the simultaneous circulation in three perpendicular planes. Forming a circulation vector and studying the PDFs of the relative strength of its components, we can quantify how the mean strain enhances and orients coherent vortical structures with the streamwise direction. This is further studied with streamwise space and time correlations of the circulations over a range of loop sizes. The streamwise component of the circulation, over same-size square loops, shows increased integral length, while the other two components are less affected. The circulation around the compressive direction weakens and reaches prominent negative correlation values, suggesting buckling or sharp reorientation of transverse vortices. The PDFs of circulation transit from non-Gaussian to Gaussia

Uranus and Neptune are the least explored planets in the Solar System. A key question regarding the two planets is the similarity of their observed flows despite the great differences in their obliquity and internal heating. To answer this fundamental question and understand the ice giants atmospheric circulation, we developed a new general circulation model (GCM). This tool will also be key to facilitating the success of future missions to the ice giants, for which atmospheric flows will be a measurable quantity. Past GCMs for the ice giants have struggled to reproduce the observed winds on Uranus and Neptune. Using our idealized GCM, we systematically explored how the zonal wind and meridional circulation respond to different model and physical parameters; our main focus was on the depth of the domain. We show that in cases where the bottom layer of the model is deep enough, the simulated flow is independent of the meridional structure of the forcing temperature, indicating that dynamical processes, and not the imposed thermal forcing, are the dominant drivers of the circulation and the thermal structure. A momentum balance analysis further shows that meridional and vertical eddy

We present a new optimization-based method for aggregating preferences in settings where each voter expresses preferences over pairs of alternatives. Our approach to identifying a consensus partial order is motivated by the observation that collections of votes that form a cycle can be treated as collective ties. Our approach then removes unions of cycles of votes, or circulations, from the vote graph and determines aggregate preferences from the remainder. Specifically, we study the removal of maximal circulations attained by any union of cycles the removal of which leaves an acyclic graph. We introduce the strong maximum circulation, the removal of which guarantees a unique outcome in terms of the induced partial order, called the strong partial order. The strong maximum circulation also satisfies strong complementary slackness conditions, and is shown to be solved efficiently as a network flow problem. We further establish the relationship between the dual of the maximum circulation problem and Kemeny's method, a popular optimization-based approach for preference aggregation. We also show that identifying a minimum maximal circulation -- i.e., a maximal circulation containing th

We investigate how the meridional circulation and baroclinic eddies change with insolation and rotation rate, under high and zero obliquity setups, using a general circulation model. The total circulation is considered as superposition of circulations driven by different physics processes, such as diabatic and adiabatic processes. We decompose the meridional circulation into diabatic and adiabatic components, in order to understand their different responses to changes of insolation and rotation rate. As insolation or rotation period increases, the meridional circulation tends to become more diabatically dominant, regardless of the obliquity. The low obliquity circulation is always dominated by diabatic processes, while the high obliquity configuration has two circulation regimes: an adiabatic-dominant regime in the limit of low insolation and fast rotation, and a diabatic-dominant regime in the opposite limit. This regime transition may be observable via its signature on the upper atmospheric zonal wind and the column cloud cover. The momentum-driven circulation, the dominant circulation component in the weak-insolation and fast-rotating regimes is found to resemble that in a dry d

Time-dependent meridional circulation and differential rotation in radiative zones are central open issues in stellar evolution theory. We streamline this challenging problem using the downward control principle of atmospheric science, under a geostrophic f-plane approximation. We recover the known stellar physics result that the steady-state meridional circulation decays on the length scale proportional to N/f sqrt(Pr), assuming molecular viscosity is the dominant drag mechanism. Prior to steady-state, the meridional circulation and the zonal wind (= differential rotation) spread together via radiative diffusion, under thermal wind balance. The corresponding (4th-order) hyperdiffusion process is reasonably well approximated by regular (2nd-order) diffusion on scales of order a pressure scale-height. We derive an inhomogeneous diffusion (equiv. advection-diffusion) equation for the zonal flow which admits closed-form time-dependent solutions in a finite depth domain, allowing for rapid prototyping of differential rotation profiles. In the weak drag limit, we find that the time to rotational steady-state can be longer than the Eddington-Sweet time and be instead determined by the lo

Circulation is the characteristic feature of successful currency systems, from community currencies to cryptocurrencies to national currencies. In this paper, we propose a network analysis approach especially suited for studying circulation given a system's digital transaction records. Sarafu is a digital community currency that was active in Kenya over a period that saw considerable economic disruption due to the COVID-19 pandemic. We represent its circulation as a network of monetary flow among the 40,000 Sarafu users. Network flow analysis reveals that circulation was highly modular, geographically localized, and occurring among users with diverse livelihoods. Across localized sub-populations, network cycle analysis supports the intuitive notion that circulation requires cycles. Moreover, the sub-networks underlying circulation are consistently degree disassortative and we find evidence of preferential attachment. Community-based institutions often take on the role of local hubs, and network centrality measures confirm the importance of early adopters and of women's participation. This work demonstrates that networks of monetary flow enable the study of circulation within curren

Gyres are central features of large-scale ocean circulation and are involved in transporting tracers such as heat, nutrients, and carbon-dioxide within and across ocean basins. Traditionally, the gyre circulation is thought to be driven by surface winds and quantified via Sverdrup balance, but it has been proposed that surface buoyancy fluxes may also contribute to gyre forcing. Through a series of eddy-permitting global ocean model simulations with perturbed surface forcing, the relative contribution of wind stress and surface heat flux forcing to the large-scale ocean circulation is investigated, focusing on the subtropical gyres. In addition to gyre strength being linearly proportional to wind stress, it is shown that the gyre circulation is strongly impacted by variations in the surface heat flux (specifically, its meridional gradient) through a rearrangement of the ocean's buoyancy structure. On shorter timescales ($\sim$ decade), the gyre circulation anomalies are proportional to the magnitude of the surface heat flux gradient perturbation, with up to $\sim 0.15\,\mathrm{Sv}$ anomaly induced per $\mathrm{W}\,\mathrm{m}^{-2}$ change in the surface heat flux. On timescales long

The general circulation of the atmosphere determines the long-term variability of weather processes. This circulation is driven by the temperature differences between the poles and the equator, causing air to move along the Earth's surface. However, this requires enhanced pressure at the poles, which is not observed. To sustain the circulation, an additional non-hydrostatic pressure gradient is required. In my research, I propose the emergence of an additional non-hydrostatic pressure gradient resulting from the centrifugal force generated by the Earth's rotation. This centrifugal force creates a non-hydrostatic vertical pressure gradient, which is essential for the closed circulation of unequally heated air in the meridional direction. The circulation is composed of three distinct streams flowing in opposite directions, with the polar and tropical tropopause acting as boundaries. The temperature in the atmosphere decreases from the surface to the polar tropopause and remains constant above it.

Internal recirculation in a moving droplet plays an important role in several droplet-based microfluidic devices as it enhances mixing, chemical reaction and heat transfer. The occurrence of fluid slip at the wall, which becomes prominent at high shear rates and lower length scales, results in a significant change in droplet circulation. Using molecular dynamics (MD) simulations, the presence of circulation in droplets is demonstrated and quantified. Circulation is shown to vary inversely with slip length, which is a measure of interface wettability. A simple circulation model is established that captures the effect of slip on droplet circulation. Scaling parameters for circulation and slip length are identified from the circulation model which leads to the collapse of data for droplets with varying aspect ratio (AR) and slip length. The model is validated using continuum and MD simulations and is shown to be accurate for droplets with high AR.

The ocean thermohaline circulation, also called meridional overturning circulation, is caused by water density contrasts. This circulation has large capacity of carrying heat around the globe and it thus affects the energy budget and further affects the climate. We consider a thermohaline circulation model in the meridional plane under external wind forcing. We show that, when there is no wind forcing, the stream function and the density fluctuation (under appropriate metrics) tend to zero exponentially fast as time goes to infinity. With rapidly oscillating wind forcing, we obtain an averaging principle for the thermohaline circulation model. This averaging principle provides convergence results and comparison estimates between the original thermohaline circulation and the averaged thermohaline circulation, where the wind forcing is replaced by its time average. This establishes the validity for using the averaged thermohaline circulation model for numerical simulations at long time scales.

The Hadley circulation (or Hadley cell) is traditionally described as a large-scale atmospheric circulation phenomenon driven by differential heating of the Earth surface: warm, moist air rises near the equator, diverges poleward in the upper troposphere, and subsides in the subtropics. In this article, the mechanism of the Hadley circulation is revisited and a new model is provided to explain its mechanism. The new model is based on a form of the atmospheric dynamic equation which substitutes pressure with temperature and density; thereby categorizing weather systems into thermal and dynamic systems. Such classification is useful for explaining large-scale weather systems such as the Hadley cell. The proposed explanation for the mechanism of the Hadley circulation argues that subtropical highs are the driving force of the Hadley cell, rather than the conventionally-believed ITCZ (Intertropical Convergence Zone). To support our theory, we analyze the atmospheric air density flux divergence with the results from the Community Earth System Model (CESM) and derive a new continuity equation by adding source/sink terms, in which evaporation serves as the air-mass source, and precipitati

A loss in circulation is sometimes cited in connection with bluff-body wakes as a result of comparing the circulation actually observed downstream with a well-known theoretical estimate of the total circulation generated by a cylinder. In an effort to better understand this reported loss in circulation, an alternative estimate of the circulation generated by a cylinder is derived by integrating the velocity on a closed loop containing the attached boundary layer. Predictions of the dimensionless circulation for a cylinder in cross flow are less than the previous theoretical estimate and agree with observed values. This suggests that the total circulation generated by bluff bodies may have been overestimated in the past, and that comparison of observed values with this overestimate is the origin of the perceived "loss" in circulation.

The general circulation of the atmosphere determines the long-term variability of weather processes. This circulation is driven by the temperature differences between the poles and the equator, causing air to move along the Earth's surface. However, this requires enhanced pressure at the poles, which is not observed. To sustain the circulation, an additional non-hydrostatic pressure gradient is required. Here I propose the emergence of an additional non-hydrostatic pressure gradient resulting from the centrifugal force generated by the Earth's rotation. This centrifugal force creates a non-hydrostatic vertical pressure gradient, which is essential for the closed circulation of unequally heated air in the meridional direction. The circulation is composed of three distinct streams flowing in opposite directions, with the polar and tropical tropopause acting as boundaries. The temperature in the atmosphere decreases from the surface to the polar tropopause and remains constant above it.

Globally ice-covered oceans have been found on multiple moons in the solar system and may also have been a feature of Earth's past. However, relatively little is understood about the dynamics of these ice-covered oceans, which affect not only the physical environment but also any potential life and its detectability. A number of studies have simulated the circulation of icy-world oceans, but have come to seemingly widely different conclusions. To better understand and narrow down these diverging results, we discuss energetic constraints for the circulation on ice-covered oceans, focusing in particular on Snowball Earth, Europa, and Enceladus. Energy input that can drive ocean circulation on ice-covered bodies can be associated with heat and salt fluxes at the boundaries as well as ocean tides and librations. We show that heating from the solid core balanced by heat loss through the ice sheet can drive an ocean circulation, but the resulting flows would be relatively weak and strongly affected by rotation. Salt fluxes associated with freezing and melting at the ice sheet boundary are unlikely to energetically drive a circulation, although they can shape the large-scale circulation w