scholarly journals Unsteady chains of wave structures and anomalous transport of а passive scalar in a barotropic jet flow

2019 ◽  
Vol 55 (6) ◽  
pp. 201-210
Author(s):  
V. P. Reutov ◽  
G. V. Rybushkina
Keyword(s):  
Complex Dynamics ◽  
Tracer Particle ◽  
Pseudospectral Method ◽  
Passive Scalar ◽  
Jet Flow ◽  
Anomalous Transport ◽  
Zonal Flows ◽  
Beta Effect ◽  
Two Dimensional Flow ◽  
And Diffusion

The onset of anomalous transport of a passive scalar at the excitation of unsteady chains of wave structures with closed streamlines in a barotropic jet flow modeling zonal flows in the Earths atmosphere and ocean and in laboratory experiments is investigated. The analysis is performed within a dynamical model describing saturation of the barotropic instability in a plane-parallel channel flow with allowance for the beta-effect and external friction. The equations of a quasi-two-dimensional flow are solved numerically with the aid of a pseudospectral method. It is found that the generation of high modes in a jet with a two-hump velocity profile leads to accelerated transition to the complex dynamics, at which an increase in supercriticality first gives rise to а multiharmonic regime with a discrete spectrum. The exponents of the power dependence on the time of the averaged (over the ensemble) tracer particle displacement and its variance are computed for the basic generation regimes, which confirms the occurrence of anomalous diffusion of the scalar. A self-similar probability density function of tracer displacements is obtained and the dependence of the transition to complex dynamics on the number of vortices in the chain and on the strength of the beta-effect is elucidated. Numerical estimates are presented, which confirm the possibility of generation of unsteady vortex chains and the related anomalous transport of the scalar.barotropic flow; chains of wave structures; dynamical chaos; anomalous advection and diffusion

scholarly journals Dynamical Model for the Anomalous Transport of a Passive Scalar in a Reverse Barotropic Jet Flow

2019 ◽  
Vol 15 (3) ◽  
pp. 251-260 ◽  
Author(s):  
V. Reutov ◽  
◽  
G.V. Rybushkina ◽  
Keyword(s):  
Passive Scalar ◽  
Jet Flow ◽  
Anomalous Transport ◽  
Dynamical Model

The diffusing-velocity random walk: Capturing the interplay of diffusion and heterogeneous advection within a spatial-Markov framework

2021 ◽  
Author(s):  
Tomas Aquino ◽  
Tanguy Le Borgne
Keyword(s):  
Shear Rate ◽  
Correlation Length ◽  
Scaling Laws ◽  
Heterogeneous Media ◽  
Tracer Particle ◽  
Diffusive Dynamics ◽  
Temporal Process ◽  
The Impact ◽  
And Diffusion

<p>The spatial distribution of a solute undergoing advection and diffusion is impacted by the velocity variability sampled by tracer particles. In spatially structured velocity fields, such as porous medium flows, Lagrangian velocities along streamlines are often characterized by a well-defined correlation length and can thus be described by spatial-Markov processes. Diffusion, on the other hand, is generally modeled as a temporal process, making it challenging to capture advective and diffusive dynamics in a single framework. In order to address this limitation, we have developed a description of transport based on a spatial-Markov velocity process along Lagrangian particle trajectories, incorporating the effect of diffusion as a local averaging process in velocity space. The impact of flow structure on this diffusive averaging is quantified through an effective shear rate. The latter is fully determined by the point statistics of velocity magnitudes together with characteristic longitudinal and transverse lengthscales associated with the flow field. For infinite longitudinal correlation length, our framework recovers Taylor dispersion, and in the absence of diffusion it reduces to a standard spatial-Markov velocity model. This novel framework allows us to derive dynamical equations governing the evolution of particle position and velocity, from which we obtain scaling laws for the dependence of longitudinal dispersion on Péclet number. Our results provide new insights into the role of shear and diffusion on dispersion processes in heterogeneous media.</p><p>In this presentation, I propose to discuss: (i) Spatial-Markov models and the modeling of diffusion as a spatial rather than temporal process; (ii) The concept of the effective shear rate and its role in the diffusive dynamics of tracer particle velocities; (iii) The role of transverse diffusion and its interplay with velocity heterogeneity on longitudinal solute dispersion.</p>

Gravitational Diffusion From a Boundary Source in Two-Dimensional Flow

1947 ◽  
Vol 14 (3) ◽  
pp. A225-A228
Author(s):  
Hunter Rouse
Keyword(s):  
Ground Level ◽  
Specific Weight ◽  
Error Distribution ◽  
Heated Air ◽  
Boundary Source ◽  
Two Dimensional Flow ◽  
Important Means ◽  
Heat Requirements ◽  
Direct Proportionality ◽  
And Diffusion

Abstract Convection currents of heated air downwind from a continuous line of gasoline burners at ground level provided an important means of dispersing fog over airfields during the recent war. A study of heat requirements as a function of burner location and cross-wind velocity, conducted by the Iowa Institute of Hydraulic Research in 1943, yielded results which are considered applicable to all similar problems of gravitational diffusion from a boundary source—such, for instance, as the mixing through induced convection of sediment-laden water introduced at the upper surface of a stream. The author presents herewith a general analysis of the problem, based upon solution of the differential equations of energy and diffusion for the assumption of (1) an error distribution of the specific-weight difference over any normal section and (2) a direct proportionality between the mixing length and the standard deviation of the error curve. Experimental results are shown to verify the analysis with good approximation.

Martian methane plume models for defining Mars rover methane source search strategies

2018 ◽  
Vol 17 (3) ◽  
pp. 228-238 ◽  
Author(s):  
Christopher Nicol ◽  
Alex Ellery ◽  
Brian Lynch ◽  
Ed Cloutis ◽  
Guido de Croon
Keyword(s):  
Search Strategy ◽  
Complex Dynamics ◽  
Search Strategies ◽  
Atmospheric Methane ◽  
Mars Rover ◽  
Gradient Based ◽  
Sophisticated Model ◽  
Methane Source ◽  
Near Term ◽  
And Diffusion

AbstractThe detection of atmospheric methane on Mars implies an active methane source. This introduces the possibility of a biotic source with the implied need to determine whether the methane is indeed biotic in nature or geologically generated. There is a clear need for robotic algorithms which are capable of manoeuvring a rover through a methane plume on Mars to locate its source. We explore aspects of Mars methane plume modelling to reveal complex dynamics characterized by advection and diffusion. A statistical analysis of the plume model has been performed and compared to analyses of terrestrial plume models. Finally, we consider a robotic search strategy to find a methane plume source. We find that gradient-based techniques are ineffective, but that more sophisticated model-based search strategies are unlikely to be available in near-term rover missions.

THEORY OF RANDOM ADVECTION IN TWO DIMENSIONS

1996 ◽  
Vol 10 (18n19) ◽  
pp. 2273-2309 ◽  
Author(s):  
M. CHERTKOV ◽  
G. FALKOVICH ◽  
I. KOLOKOLOV ◽  
V. LEBEDEV
Keyword(s):  
Velocity Field ◽  
Probability Distribution ◽  
Probability Distributions ◽  
Classical Problem ◽  
Passive Scalar ◽  
Two Dimensions ◽  
Change Of Variables ◽  
The Matrix ◽  
Two Dimensional Flow ◽  
Non Gaussian

The steady statistics of a passive scalar advected by a random two-dimensional flow of an incompressible fluid is described at scales less than the correlation length of the flow and larger than the diffusion scale. The probability distribution of the scalar is expressed via the probability distribution of the line stretching rate. The description of the line stretching can be reduced to the classical problem of studying the product of many matrices with a unit determinant. We found a change of variables which allows one to map the matrix problem into a scalar one and to prove thus a central limit theorem for the statistics of the stretching rate. The proof is valid for any finite correlation time of the velocity field. Whatever be the statistics of the velocity field, the statistics of the passive scalar in the inertial interval of scales is shown to approach Gaussianity as one increases the Peclet number Pe (the ratio of the pumping scale to the diffusion one). The first n < ln (Pe) simultaneous correlation functions are expressed via the flux of the squared scalar and only one unknown factor depending on the velocity field: the mean stretching rate. That factor can be calculated analytically for the limiting cases. The non-Gaussian tails of the probability distributions at finite Pe are found to be exponential.

scholarly journals Anomalous Transport: A Mathematical Framework

1998 ◽  
Vol 10 (01) ◽  
pp. 1-46 ◽  
Author(s):  
H. Schulz-Baldes ◽  
J. Bellissard
Keyword(s):  
Transport Properties ◽  
Anderson Model ◽  
Coherent Potential Approximation ◽  
Anomalous Transport ◽  
Mathematical Framework ◽  
Spectral Measures ◽  
Potential Approximation ◽  
And Diffusion

We develop a mathematical framework allowing to study anomalous transport in homogeneous solids. The main tools characterizing the anomalous transport properties are spectral and diffusion exponents associated to the covariant Hamiltonians describing these media. The diffusion exponents characterize the spectral measures entering in Kubo's formula for the conductivity and hence lead to anomalies in Drude's formula. We give several formulas allowing to calculate these exponents and treat, as an example, Wegner's n-orbital model as well as the Anderson model in coherent potential approximation.

scholarly journals Dynamical Chaos and Lateral Transport of a Passive Scalar in the Annular Reverse Jet Flow

2021 ◽  
Vol 17 (3) ◽  
pp. 263-274
Author(s):  
V. P. Reutov ◽  
◽  
G. V. Rybushkina ◽  
Keyword(s):  
Lyapunov Exponent ◽  
Cross Flow ◽  
Passive Scalar ◽  
Jet Flow ◽  
Wave Generation ◽  
Critical Parameters ◽  
Dynamical Chaos ◽  
Lateral Transport ◽  
Frequency Spectra ◽  
Flow Transport

The transition to dynamical chaos and the related lateral (cross-flow) transport of a passive scalar in the reverse annular jet flow generating two chains of wave-vortex structures are studied. The quasi-geostrophic equations for the barotropic (quasi-two-dimensional) flow written in polar coordinates with allowance for the beta-effect and external friction are solved numerically using a pseudospectral method. The critical parameters of the equilibrium flow with a complex “two-hump” azimuth velocity profile facilitating a faster transition to the complex dynamics are determined. Two regular multiharmonic regimes of wave generation are revealed with increasing flow supercriticality before the onset of Eulerian chaos. The occurrence of the complex flow dynamics is confirmed by a direct calculation of the largest Lyapunov exponent. The evolution of streamline images is analyzed by making video, thereby chains with single and composite structures are distinguished. The wavenumber-frequency spectra confirming the possibility of chaotic transport of the passive scalar are drawn for the basic regimes of wave generation. The power law exponents for the azimuth particle displacement and their variance, which proved the occurrence of the anomalous azimuth transport of the passive scalar, are determined. Lagrangian chaos is studied by computing the finite-time Lyapunov exponent and its distribution function. The internal chain (with respect to the annulus center) is found to be totally subject to Lagrangian chaos, while only the external chain boundary is chaotic. It is revealed that the cross-flow transport occurs only in the regime of Eulerian dynamical chaos, since there exists a barrier to it in the multiharmonic regimes. The images of fluid particles confirming the presence of lateral transport are obtained and their quantitative characteristics are determined.

Sign in / Sign up

Export Citation Format

Share Document