1,513 research outputs found
Active vs passive scalar turbulence
Active and passive scalars transported by an incompressible two-dimensional
conductive fluid are investigated. It is shown that a passive scalar displays a
direct cascade towards the small scales while the active magnetic potential
builds up large-scale structures in an inverse cascade process. Correlations
between scalar input and particle trajectories are found to be responsible for
those dramatic differences as well as for the behavior of dissipative
anomalies.Comment: Revised version, Phys. Rev. Lett., in pres
Monotonic Distributive Semilattices
In the study of algebras related to non-classical logics, (distributive) semilattices are always present in the background. For example, the algebraic semantic of the {→, ∧, ⊤}-fragment of intuitionistic logic is the variety of implicative meet-semilattices (Chellas 1980; Hansen 2003). In this paper we introduce and study the class of distributive meet-semilattices endowed with a monotonic modal operator m. We study the representation theory of these algebras using the theory of canonical extensions and we give a topological duality for them. Also, we show how our new duality extends to some particular subclasses.Fil: Celani, Sergio Arturo. Consejo Nacional de Investigaciones CientÃficas y Técnicas; Argentina. Universidad Nacional del Centro de la Provincia de Buenos Aires. Facultad de Ciencias Exactas. Departamento de Matemática; ArgentinaFil: Menchón, MarÃa Paula. Universidad Nacional del Centro de la Provincia de Buenos Aires. Facultad de Ciencias Exactas. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones CientÃficas y Técnicas; Argentin
Front propagation in laminar flows
The problem of front propagation in flowing media is addressed for laminar
velocity fields in two dimensions. Three representative cases are discussed:
stationary cellular flow, stationary shear flow, and percolating flow.
Production terms of Fisher-Kolmogorov-Petrovskii-Piskunov type and of Arrhenius
type are considered under the assumption of no feedback of the concentration on
the velocity. Numerical simulations of advection-reaction-diffusion equations
have been performed by an algorithm based on discrete-time maps. The results
show a generic enhancement of the speed of front propagation by the underlying
flow. For small molecular diffusivity, the front speed depends on the
typical flow velocity as a power law with an exponent depending on the
topological properties of the flow, and on the ratio of reactive and advective
time-scales. For open-streamline flows we find always , whereas for
cellular flows we observe for fast advection, and for slow advection.Comment: Enlarged, revised version, 37 pages, 14 figure
Shear effects on passive scalar spectra
The effects of a large-scale shear on the energy spectrum of a passively
advected scalar field are investigated. The shear is superimposed on a
turbulent isotropic flow, yielding an Obukhov-Corrsin scalar
spectrum at small scales. Shear effects appear at large scales, where a
different, anisotropic behavior is observed. The scalar spectrum is shown to
behave as for a shear fixed in intensity and direction. For other
types of shear characteristics, the slope is generally intermediate between the
-5/3 Obukhov-Corrsin's and the -1 Batchelor's values. The physical mechanisms
at the origin of this behaviour are illustrated in terms of the motion of
Lagrangian particles. They provide an explanation to the scalar spectra shallow
and dependent on the experimental conditions observed in shear flows at
moderate Reynolds numbers.Comment: 10 LaTeX pages,3 eps Figure
Large-Eddy Simulation closures of passive scalar turbulence: a systematic approach
The issue of the parameterization of small scale (``subgrid'') turbulence is
addressed in the context of passive scalar transport. We focus on the Kraichnan
advection model which lends itself to the analytical investigation of the
closure problem. We derive systematically the dynamical equations which rule
the evolution of the coarse-grained scalar field. At the lowest-order
approximation in , being the characteristic scale of the filter
defining the coarse-grained scalar field and the inertial range separation,
we recover the classical eddy-diffusivity parameterization of small scales. At
the next-leading order a dynamical closure is obtained. The latter outperforms
the classical model and is therefore a natural candidate for subgrid modelling
of scalar transport in generic turbulent flows.Comment: 10 LaTex pages, 1 PS figure. Changes: comments added below previous
(3.10); Previous (3.16) has been corrected; Minor changes in the conclusion
Scaling and universality in turbulent convection
Anomalous correlation functions of the temperature field in two-dimensional
turbulent convection are shown to be universal with respect to the choice of
external sources. Moreover, they are equal to the anomalous correlations of the
concentration field of a passive tracer advected by the convective flow itself.
The statistics of velocity differences is found to be universal, self-similar
and close to Gaussian. These results point to the conclusion that temperature
intermittency in two-dimensional turbulent convection may be traced back to the
existence of statistically preserved structures, as it is in passive scalar
turbulence.Comment: 4 pages, 6 figure
The predictability problem in systems with an uncertainty in the evolution law
The problem of error growth due to the incomplete knowledge of the evolution
law which rules the dynamics of a given physical system is addressed. Major
interest is devoted to the analysis of error amplification in systems with many
characteristic times and scales. The importance of a proper parameterization of
fast scales in systems with many strongly interacting degrees of freedom is
highlighted and its consequences for the modelization of geophysical systems
are discussed.Comment: 20 pages RevTeX, 6 eps figures (included
Non Asymptotic Properties of Transport and Mixing
We study relative dispersion of passive scalar in non-ideal cases, i.e. in
situations in which asymptotic techniques cannot be applied; typically when the
characteristic length scale of the Eulerian velocity field is not much smaller
than the domain size. Of course, in such a situation usual asymptotic
quantities (the diffusion coefficients) do not give any relevant information
about the transport mechanisms. On the other hand, we shall show that the
Finite Size Lyapunov Exponent, originally introduced for the predictability
problem, appears to be rather powerful in approaching the non-asymptotic
transport properties. This technique is applied in a series of numerical
experiments in simple flows with chaotic behaviors, in experimental data
analysis of drifter and to study relative dispersion in fully developed
turbulence.Comment: 19 RevTeX pages + 8 figures included, submitted on Chaos special
issue on Transport and Mixin
Clustering and collisions of heavy particles in random smooth flows
Finite-size impurities suspended in incompressible flows distribute
inhomogeneously, leading to a drastic enhancement of collisions. A description
of the dynamics in the full position-velocity phase space is essential to
understand the underlying mechanisms, especially for polydisperse suspensions.
These issues are here studied for particles much heavier than the fluid by
means of a Lagrangian approach. It is shown that inertia enhances collision
rates through two effects: correlation among particle positions induced by the
carrier flow and uncorrelation between velocities due to their finite size. A
phenomenological model yields an estimate of collision rates for particle pairs
with different sizes. This approach is supported by numerical simulations in
random flows.Comment: 12 pages, 9 Figures (revTeX 4) final published versio
Variable-time-domain neighboring optimal guidance and attitude control of low-thrust lunar orbit transfers
Lunar orbit dynamics and transfers at low altitudes are subject to considerable perturbations related to the gravitational harmonics associated with the irregular lunar mass distribution. This research proposes the original combination of two techniques applied to low-thrust lunar orbit transfers, i.e. (i) the variable-time-domain neighboring optimal guidance (VTD-NOG), and (ii) a proportional-derivative attitude control algorithm based on rotation matrices (PD-RM). VTD-NOG belongs to the class of feedback implicit guidance approaches, aimed at maintaining the spacecraft sufficiently close to the reference trajectory. This is an optimal path that satisfies the second-order sufficient conditions for optimality. A fundamental original feature of VTD-NOG is the use of a normalized time scale, with the favorable consequence that the gain matrices remain finite for the entire time of flight. VTD-NOG identifies the trajectory corrections by assuming the thrust direction as the control input. Because the thrust direction is fixed with respect to the spacecraft, VTD-NOG generates the desired orientation pursued by the attitude control system. A proportional-derivative approach using rotation matrices (PD-RM) is employed in order to drive the actual spacecraft orientation toward the desired one. Reaction wheels are considered as the actuators that perform attitude control. Extensive Monte Carlo simulations are performed, in the presence of nonnominal flight conditions related to (i) lunar gravitational harmonics, (ii) gravitational pull of the Earth and the Sun as third bodies, (iii) unpredictable propulsive fluctuations, and (iv) errors on initial attitude. The numerical results unequivocally demonstrate that the joint use of VTD-NOG and PD-RM control represents an accurate and effective methodology for guidance and control of low-thrust lunar orbit transfers
- …