Important statistical properties of velocity circulation in homogeneous isotropic turbulence (HIT) have been unveiled in recent years, raising the question of whether they persist, or are modified, in other classes of turbulent flows. Motivated by the dominant role of small-scale structures in the circulation fluctuations of HIT, we investigate their relevance in direct numerical simulations of Rayleigh-Bénard convection at a Rayleigh number of $10^9$ and Prandtl number of $O(1)$. Within the thermal boundary layer (TBL), the distribution of elementary vortices is found to be strongly correlated with the temperature field, while the statistics of their core aspect ratios is significantly altered. Additionally, the probability distribution functions of circulation, computed for planar contours which are parallel to the walls, display salient features closely akin to those observed in HIT, with the {\it Area Rule} (a connection between circulation statistics and minimal surfaces) remaining particularly well satisfied -- except for a possible transitional region at a distance of a few TBL thicknesses. Away from the TBL, as expected, the overall statistical behavior of these structures
Recent investigations of turbulent circulation fluctuations have uncovered substantial insights into the statistical organization of flow structures and revealed unexpected geometric features of turbulent intermittency. Of particular interest here is the observation that circulation probability distribution functions admit a superstatistical representation, namely a description based on "ensembles of Boltzmann-Gibbs ensembles". A fundamental phenomenological ingredient of this approach, which serves as a natural starting point for modeling, relies on the strong correlation between the dissipation field and the spatial distribution of elementary circulation-carrying structures, i.e., small-scale vortices. Within the language of superstatistics, this corresponds to characterizing circulation statistics through an appropriate choice of conditioned (Boltzmann-like) distributions and mixing distributions. We show that the superstatistical class of q-exponentials, known to have broad applicability in a wide range of multiscale and non-equilibrium systems, provides an accurate description of the observed circulation statistics in homogeneous and isotropic turbulence. This finding opens av
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.
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 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
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 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
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.
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
Observations of time-resolved thermal emission from tidally locked exoplanets can tell us about their atmospheric temperature structure. Telescopes such as JWST and ARIEL will improve the quality and availability of these measurements. This motivates an improved understanding of the processes that determine atmospheric temperature structure, particularly atmospheric circulation. The circulation is important in determining atmospheric temperatures, not only through its ability to transport heat, but also because any circulation pattern needs to be balanced by horizontal pressure contrasts, therefore implying a particular temperature structure. In this work, we show how the global temperature field on a tidally locked planet can be decomposed into contributions that are balanced by different components of the atmospheric circulation. These are the superrotating jet, stationary Rossby waves, and the divergent circulation. To achieve this, we partition the geopotential field into components balanced by the divergent circulation and the rotational circulation, with the latter comprising the jet and Rossby waves. The partitioned geopotential then implies a corresponding partitioning of t
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
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.
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
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.
Persistent circulation is a canonical effect of superfluidity. In previous experiments, quantized circulation has been observed in polariton condensates, usually far from equilibrium, but persistent current in the absence of any stirring has not been seen. We report here the direct observation of persistent circulation of a polariton condensate with no driving force and with no observable change in time. We can cause the condensate to circulate in either direction on demand using a short laser pulse, after which the condensate continues to circulate for dozens to hundreds of rotations around a ring trap without any further stimulation. Our theoretical model successfully shows how the pulse, despite not carrying any angular momentum, causes the circulation.
Using a 3D general circulation model, we demonstrate that a confirmed rocky exoplanet and a primary observational target, TRAPPIST-1e presents an interesting case of climate bistability. We find that the atmospheric circulation on TRAPPIST-1e can exist in two distinct regimes for a 1~bar nitrogen-dominated atmosphere. One is characterized by a single strong equatorial prograde jet and a large day-night temperature difference; the other is characterized by a pair of mid-latitude prograde jets and a relatively small day-night contrast. The circulation regime appears to be highly sensitive to the model setup, including initial and surface boundary conditions, as well as physical parameterizations of convection and cloud radiative effects. We focus on the emergence of the atmospheric circulation during the early stages of simulations and show that the regime bistability is associated with a delicate balance between the zonally asymmetric heating, mean overturning circulation, and mid-latitude baroclinic instability. The relative strength of these processes places the GCM simulations on different branches of the evolution of atmospheric dynamics. The resulting steady states of the two r