Exact two-dimensionalization of low-magnetic-Reynolds-number flows subject to a strong magnetic field

We investigate the behavior of flows, including turbulent flows, driven by a horizontal body-force and subject to a vertical magnetic field, with the following question in mind: for very strong applied magnetic field, is the flow mostly two-dimensional, with remaining weak three-dimensional fluctuations, or does it become exactly 2D, with no dependence along the vertical? We first focus on the quasi-static approximation, i.e. the asymptotic limit of vanishing magnetic Reynolds number Rm << 1: we prove that the flow becomes exactly 2D asymptotically in time, regardless of the initial condition and provided the interaction parameter N is larger than a threshold value. We call this property "absolute two-dimensionalization": the attractor of the system is necessarily a (possibly turbulent) 2D flow. We then consider the full-magnetohydrodynamic equations and we prove that, for low enough Rm and large enough N, the flow becomes exactly two-dimensional in the long-time limit provided the initial vertically-dependent perturbations are infinitesimal. We call this phenomenon "linear two-dimensionalization": the (possibly turbulent) 2D flow is an attractor of the dynamics, but it is not necessarily the only attractor of the system. Some 3D attractors may also exist and be attained for strong enough initial 3D perturbations. These results shed some light on the existence of a dissipation anomaly for magnetohydrodynamic flows subject to a strong external magnetic field.Comment: Journal of Fluid Mechanics, in pres

Refraction of swell by surface currents

Using recordings of swell from pitch-and-roll buoys, we have reproduced the classic observations of long-range surface wave propagation originally made by Munk et al. (1963) using a triangular array of bottom pressure measurements. In the modern data, the direction of the incoming swell fluctuates by about $\pm 10^\circ$ on a time scale of one hour. But if the incoming direction is averaged over the duration of an event then, in contrast with the observations by Munk et al. (1963), the sources inferred by great-circle backtracking are most often in good agreement with the location of large storms on weather maps of the Southern Ocean. However there are a few puzzling failures of great-circle backtracking e.g., in one case, the direct great-circle route is blocked by the Tuamoto Islands and the inferred source falls on New Zealand. Mirages like this occur more frequently in the bottom-pressure observations of Munk et al. (1963), where several inferred sources fell on the Antarctic continent. Using spherical ray tracing we investigate the hypothesis that the refraction of waves by surface currents produces the mirages. With reconstructions of surface currents inferred from satellite altimetry, we show that mesoscale vorticity significantly deflects swell away from great-circle propagation so that the source and receiver are connected by a bundle of many rays, none of which precisely follow a great circle. The $\pm 10^\circ$ directional fluctuations at the receiver result from the arrival of wave packets that have travelled along the different rays within this multipath. The occasional failure of great-circle backtracking, and the associated mirages, probably results from partial topographic obstruction of the multipath, which biases the directional average at the receiver.Comment: Journal of Marine Research, in pres

Syntax directed analysis of liveness properties of while programs

A syntax directed proof system which allows to prove liveness properties of while-programs is introduced. The proof system is proved to be arithmetically sound and complete in the sense of Harel (“Lecture Notes in Comput. Sci. Vol. 68,” Springer-Verlag, Berlin/New York, 1979). The results of the paper generalize a corresponding result Pneuli (“Prc. 18th Sympos. FOCS” IEEE, Providence, R. I., 1977) proves for unstructured programs. The proof system decomposes into two parts. The first part allows to prove simple safety properties. These properties are used as axioms in the second proof system which deals with liveness properties. The completeness proof is constructive and provides a heuristic for proving specific liveness properties

Empirical scaling of antisymmetric stratified wakes

Proceedings of the "Bluff Body Wakes and Vortex-Induced Vibrations - BBVIV-4"Initially turbulent wakes of a propelled cylinder at nonzero angles of yaw to the mean flow were measured in the horizontal centerplane plane up to approximately 100 buoyancy times, where vertical velocities are very small. The profiles of mean velocity were found to be antisymmetric throughout their lifetime, with both width and maximum velocity decaying at the same rate as previously studied momentum wakes. The maximum velocity of the profile is proportional to the angle of yaw, but the width is constant. Both the mean flow and fluctuating quantities show that the late wake is self-similar, with scaling laws that are consistent with previous work on propelled and drag wakes

Destabilizing Taylor-Couette flow with suction

We consider the effect of radial fluid injection and suction on Taylor-Couette flow. Injection at the outer cylinder and suction at the inner cylinder generally results in a linearly unstable steady spiralling flow, even for cylindrical shears that are linearly stable in the absence of a radial flux. We study nonlinear aspects of the unstable motions with the energy stability method. Our results, though specialized, may have implications for drag reduction by suction, accretion in astrophysical disks, and perhaps even in the flow in the earth's polar vortex.Comment: 34 pages, 9 figure

Probing active forces via a fluctuation-dissipation relation: Application to living cells

We derive a new fluctuation-dissipation relation for non-equilibrium systems with long-term memory. We show how this relation allows one to access new experimental information regarding active forces in living cells that cannot otherwise be accessed. For a silica bead attached to the wall of a living cell, we identify a crossover time between thermally controlled fluctuations and those produced by the active forces. We show that the probe position is eventually slaved to the underlying random drive produced by the so-called active forces.Comment: 5 page

Anonymous Asynchronous Systems: The Case of Failure Detectors

Due the multiplicity of loci of control, a main issue distributed systems have to cope with lies in the uncertainty on the system state created by the adversaries that are asynchrony, failures, dynamicity, mobility, etc. Considering message-passing systems, this paper considers the uncertainty created by the net effect of three of these adversaries, namely, asynchrony, failures, and anonymity. This means that, in addition to be asynchronous and crash-prone, the processes have no identity. Trivially, agreement problems (e.g., consensus) that cannot be solved in presence of asynchrony and failures cannot be solved either when adding anonymity. The paper consequently proposes anonymous failure detectors to circumvent these impossibilities. It has several contributions. First it presents three classes of failure detectors (denoted AP, A∩ and A∑) and show that they are the anonymous counterparts of the classes of perfect failure detectors, eventual leader failure detectors and quorum failure detectors, respectively. The class A∑ is new and showing it is the anonymous counterpart of the class ∑ is not trivial. Then, the paper presents and proves correct a genuinely anonymous consensus algorithm based on the pair of anonymous failure detector classes (A∩, A∑) (“genuinely” means that, not only processes have no identity, but no process is aware of the total number of processes). This new algorithm is not a “straightforward extension” of an algorithm designed for non-anonymous systems. To benefit from A∑, it uses a novel message exchange pattern where each phase of every round is made up of sub-rounds in which appropriate control information is exchanged. Finally, the paper discusses the notions of failure detector class hierarchy and weakest failure detector class for a given problem in the context of anonymous systems

Solving atomic multicast when groups crash

In this paper, we study the atomic multicast problem, a fundamental abstraction for building faulttolerant systems. In the atomic multicast problem, the system is divided into non-empty and disjoint groups of processes. Multicast messages may be addressed to any subset of groups, each message possibly being multicast to a different subset. Several papers previously studied this problem either in local area networks [3, 9, 20] or wide area networks [13, 21]. However, none of them considered atomic multicast when groups may crash. We present two atomic multicast algorithms that tolerate the crash of groups. The first algorithm tolerates an arbitrary number of failures, is genuine (i.e., to deliver a message m, only addressees of m are involved in the protocol), and uses the perfect failures detector P. We show that among realistic failure detectors, i.e., those that do not predict the future, P is necessary to solve genuine atomic multicast if we do not bound the number of processes that may fail. Thus, P is the weakest realistic failure detector for solving genuine atomic multicast when an arbitrary number of processes may crash. Our second algorithm is non-genuine and less resilient to process failures than the first algorithm but has several advantages: (i) it requires perfect failure detection within groups only, and not across the system, (ii) as we show in the paper it can be modified to rely on unreliable failure detection at the cost of a weaker liveness guarantee, and (iii) it is fast, messages addressed to multiple groups may be delivered within two inter-group message delays only

Transport and emergent stratification in the equilibrated Eady model: the vortex gas scaling regime

We numerically and theoretically investigate the Boussinesq Eady model, where a rapidly rotating density-stratified layer of fluid is subject to a meridional temperature gradient in thermal wind balance with a uniform vertically sheared zonal flow. Through a suite of numerical simulations, we show that the transport properties of the resulting turbulent flow are governed by quasi-geostrophic (QG) dynamics in the rapidly rotating strongly stratified regime. The 'vortex gas' scaling predictions put forward in the context of the two-layer QG model carry over to this fully 3D system: the functional dependence of the meridional flux on the control parameters is the same, the two ajustable parameters entering the theory taking slightly different values. In line with the QG prediction, the meridional buoyancy flux is depth-independent. The vertical buoyancy flux is such that turbulence transports buoyancy along isopycnals, except in narrow layers near the the top and bottom boundaries, the thickness of which decreases as the diffusivities go to zero. The emergent (re)stratification is set by a simple balance between the vertical buoyancy flux and diffusion along the vertical direction. Overall, this study demonstrates how the vortex-gas scaling theory can be adapted to quantitatively predict the magnitude and vertical structure of the meridional and vertical buoyancy fluxes, and of the emergent stratification, without additional fitting parameters.Comment: Accepted versio

Global Versus Local Computations: Fast Computing with Identifiers

This paper studies what can be computed by using probabilistic local interactions with agents with a very restricted power in polylogarithmic parallel time. It is known that if agents are only finite state (corresponding to the Population Protocol model by Angluin et al.), then only semilinear predicates over the global input can be computed. In fact, if the population starts with a unique leader, these predicates can even be computed in a polylogarithmic parallel time. If identifiers are added (corresponding to the Community Protocol model by Guerraoui and Ruppert), then more global predicates over the input multiset can be computed. Local predicates over the input sorted according to the identifiers can also be computed, as long as the identifiers are ordered. The time of some of those predicates might require exponential parallel time. In this paper, we consider what can be computed with Community Protocol in a polylogarithmic number of parallel interactions. We introduce the class CPPL corresponding to protocols that use $O(n\log^k n)$, for some k, expected interactions to compute their predicates, or equivalently a polylogarithmic number of parallel expected interactions. We provide some computable protocols, some boundaries of the class, using the fact that the population can compute its size. We also prove two impossibility results providing some arguments showing that local computations are no longer easy: the population does not have the time to compare a linear number of consecutive identifiers. The Linearly Local languages, such that the rational language $(ab)^*$, are not computable.Comment: Long version of SSS 2016 publication, appendixed version of SIROCCO 201