Lagrangian chaos in confined two-dimensional oscillatory convection

2014 ◽  
Vol 759 ◽  
pp. 489-519 ◽  
Author(s):  
L. Oteski ◽  
Y. Duguet ◽  
L. R. Pastur
Keyword(s):  
Coarse Graining ◽  
Chaotic Advection ◽  
Heteroclinic Orbits ◽  
Convection Flow ◽  
Two Dimensional ◽  
Unstable Periodic Orbits ◽  
Mixing Rate ◽  
Melnikov Functions ◽  
Passive Tracers ◽  
Rayleigh Numbers

AbstractThe chaotic advection of passive tracers in a two-dimensional confined convection flow is addressed numerically near the onset of the oscillatory regime. We investigate here a differentially heated cavity with aspect ratio 2 and Prandtl number 0.71 for Rayleigh numbers around the first Hopf bifurcation. A scattering approach reveals different zones depending on whether the statistics of return times exhibit exponential or algebraic decay. Melnikov functions are computed and predict the appearance of the main mixing regions via the break-up of the homoclinic and heteroclinic orbits. The non-hyperbolic regions are characterised by a larger number of Kolmogorov–Arnold–Moser (KAM) tori. Based on the numerical extraction of many unstable periodic orbits (UPOs) and their stable/unstable manifolds, we suggest a coarse-graining procedure to estimate numerically the spatial fraction of chaos inside the cavity as a function of the Rayleigh number. Mixing is almost complete before the first transition to quasi-periodicity takes place. The algebraic mixing rate is estimated for tracers released from a localised source near the hot wall.

Natural Convection for Air and Molten Gallium in Square- and Elbow-Shaped Enclosures

2015 ◽  
Vol 789-790 ◽  
pp. 462-470
Author(s):  
Emel Evren-Selamet ◽  
Ahmet Selamet
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Numerical Scheme ◽  
Lead Author ◽  
Convection Flow ◽  
Two Dimensional ◽  
Natural Convection Flow ◽  
Transfer Rates ◽  
Chaotic Flow ◽  
Rayleigh Numbers

Natural convection flow of air and molten gallium in square and elbow-shaped enclosures is studied by a two-dimensional numerical scheme developed by the lead author. The dependence of the flow field and Nusselt number (Nu) on the Rayleigh (Ra) and Prandtl (Pr) numbers is examined in both enclosures. Results are obtained with sufficiently large Rayleigh numbers to observe transition from steady to damped or undamped oscillatory, and chaotic flow. Constant and oscillatory heat transfer rates are compared in both enclosures for air (Pr=0.71) and molten gallium (Pr=0.024).

Chaotic Advection by Two-Dimensional Stokes Flow in a Semicircle

2004 ◽  
Vol 31 (4) ◽  
pp. 344-357
Author(s):  
T. A. Dunaeva ◽  
A. A. Gourjii ◽  
V. V. Meleshko
Keyword(s):  
Stokes Flow ◽  
Chaotic Advection ◽  
Two Dimensional

scholarly journals Time-Dependent Diffusion Coefficients for Chaotic Advection due to Fluctuations of Convective Rolls

Fluids ◽  
2018 ◽  
Vol 3 (4) ◽  
pp. 99 ◽  
Author(s):  
Kazuma Yamanaka ◽  
Takayuki Narumi ◽  
Megumi Hashiguchi ◽  
Hirotaka Okabe ◽  
Kazuhiro Hara ◽  
...  
Keyword(s):  
Diffusion Coefficient ◽  
Liquid Crystals ◽  
Diffusion Coefficients ◽  
Coarse Graining ◽  
Chaotic Advection ◽  
Time Dependent ◽  
Local Order ◽  
Weak Turbulence ◽  
Normal Diffusion ◽  
Convective Rolls

The properties of chaotic advection arising from defect turbulence, that is, weak turbulence in the electroconvection of nematic liquid crystals, were experimentally investigated. Defect turbulence is a phenomenon in which fluctuations of convective rolls arise and are globally disturbed while maintaining convective rolls locally. The time-dependent diffusion coefficient, as measured from the motion of a tagged particle driven by the turbulence, was used to clarify the dependence of the type of diffusion on coarse-graining time. The results showed that, as coarse-graining time increases, the type of diffusion changes from superdiffusion → subdiffusion → normal diffusion. The change in diffusive properties over the observed timescale reflects the coexistence of local order and global disorder in the defect turbulence.

Visualization and Prediction of Natural Convection of Water Near Its Density Maximum in a Tall Rectangular Enclosure at High Rayleigh Numbers

2000 ◽  
Vol 123 (1) ◽  
pp. 84-95 ◽  
Author(s):  
C. J. Ho ◽  
F. J. Tu
Keyword(s):  
Natural Convection ◽  
Vertical Wall ◽  
Three Dimensional ◽  
Temperature Fields ◽  
Convection Flow ◽  
Oscillatory Convection ◽  
Uniform Temperature ◽  
Density Maximum ◽  
Rectangular Enclosure ◽  
Rayleigh Numbers

An experimental and numerical investigation is presented concerning the natural convection of water near its maximum-density in a differentially heated rectangular enclosure at high Rayleigh numbers, in which an oscillatory convection regime may arise. The water in a tall enclosure of Ay=8 is initially at rest and at a uniform temperature below 4°C and then the temperature of the hot vertical wall is suddenly raised and kept at a uniform temperature above 4°C. The cold vertical wall is maintained at a constant uniform temperature equal to that of the initial temperature of the water. The top and bottom walls are insulated. Using thermally sensitive liquid crystal particles as tracers, flow and temperature fields of a temporally oscillatory convection was documented experimentally for RaW=3.454×105 with the density inversion parameter θm=0.5. The oscillatory convection features a cyclic sequence of onset at the lower quarter-height region, growth, and decay of the upward-drifting secondary vortices within counter-rotating bicellular flows in the enclosure. Two and three-dimensional numerical simulations corresponding to the visualization experiments are undertaken. Comparison of experimental with numerical results reveals that two-dimensional numerical simulation captures the main features of the observed convection flow.

Cellular flow in a partially filled rotating drum: regular and chaotic advection

2017 ◽  
Vol 825 ◽  
pp. 631-650 ◽  
Author(s):  
Francesco Romanò ◽  
Arash Hajisharifi ◽  
Hendrik C. Kuhlmann
Keyword(s):  
Three Dimensional ◽  
Reynolds Numbers ◽  
Chaotic Advection ◽  
Two Dimensional ◽  
Rotating Drum ◽  
Three Dimensional Flow ◽  
Dimensional Flow ◽  
Heteroclinic Connection ◽  
Two Dimensional Flow ◽  
Chaotic Streamlines

The topology of the incompressible steady three-dimensional flow in a partially filled cylindrical rotating drum, infinitely extended along its axis, is investigated numerically for a ratio of pool depth to radius of 0.2. In the limit of vanishing Froude and capillary numbers, the liquid–gas interface remains flat and the two-dimensional flow becomes unstable to steady three-dimensional convection cells. The Lagrangian transport in the cellular flow is organised by periodic spiralling-in and spiralling-out saddle foci, and by saddle limit cycles. Chaotic advection is caused by a breakup of a degenerate heteroclinic connection between the two saddle foci when the flow becomes three-dimensional. On increasing the Reynolds number, chaotic streamlines invade the cells from the cell boundary and from the interior along the broken heteroclinic connection. This trend is made evident by computing the Kolmogorov–Arnold–Moser tori for five supercritical Reynolds numbers.

Negatively Buoyant Plume Flow in a Baffled Heat Exchanger

2010 ◽  
Vol 132 (3) ◽  
Author(s):  
Sandra K. S. Boetcher ◽  
F. A. Kulacki ◽  
Jane H. Davidson
Keyword(s):  
Heat Exchanger ◽  
Effective Width ◽  
Two Dimensional ◽  
Buoyant Plume ◽  
Fully Developed Flow ◽  
Buoyant Flow ◽  
Thermal Stores ◽  
Plume Flow ◽  
Rayleigh Numbers ◽  
Negatively Buoyant

A numerical simulation of transient two-dimensional negatively buoyant flow into a straight baffle situated below an isothermal circular cylinder in an initially isothermal enclosure is presented for both an adiabatic and a highly conducting baffle for Rayleigh numbers from 106 to 107. Results show the effects of baffle offset, width, and length on the point where viscous flow develops and on velocity profiles within the baffle. Results are interpreted to guide the design of straight baffles to reduce destruction of stratification in thermal stores using an immersed heat exchanger. The preferred geometry is a low-conductivity baffle of width equal to the effective width of the heat exchanger and 15 or more cylinder diameters in length to ensure nearly fully developed flow at the baffle outlet.

Turbulence, diffusion and patchiness in the sea

1994 ◽  
Vol 343 (1303) ◽  
pp. 11-18 ◽  
Keyword(s):  
Large Scale ◽  
Approximate Model ◽  
Inertial Subrange ◽  
Biological Processes ◽  
Two Dimensional ◽  
Predator Prey ◽  
Interacting Populations ◽  
Terrestrial Environments ◽  
Population Interactions ◽  
Passive Tracers

We explore the role that biological processes play in the patchiness of plankton populations in the sea. We ask how population interactions modify the variance in plankton density as a function of spatial scale (i.e. the variance spectrum) from that expected if the biota were merely passive tracers. Using an approximate model for two limiting cases of turbulence - the inertial subrange and two-dimensional turbulence - we consider a simple predator - prey formulation for interacting populations in a turbulent ocean. No simple generalizations emerge. T he interacting populations ‘redden’ (i.e. more variance at large scale) the spectrum of the passive tracers in the inertial subrange. Conversely, the interaction ‘whitens’ (i.e. less variance at large scale) the passive tracer spectrum for two-dimensional turbulence. This mirrors results in terrestrial environments.

Transient Natural Convection Between Two Zones in an Insulated Enclosure

1988 ◽  
Vol 110 (1) ◽  
pp. 116-125 ◽  
Author(s):  
P. A. Litsek ◽  
A. Bejan
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Numerical Experiments ◽  
Thermal Stratification ◽  
Convection Flow ◽  
Natural Convection Flow ◽  
Flow And Heat Transfer ◽  
Vertical Opening ◽  
The Right ◽  
Rayleigh Numbers

The natural convection flow and heat transfer between two enclosures that communicate through a vertical opening is studied by considering the evolution of an enclosed fluid in which the left half is originally at a different temperature than the right half. Numerical experiments show that at sufficiently high Rayleigh numbers the ensuing flow is oscillatory. This and other features are anticipated on the basis of scale analysis. The time scales of the oscillation, the establishment of thermal stratification, and eventual thermal equilibrium are determined and tested numerically. At sufficiently high Rayleigh numbers the heat transfer between the communicating zones is by convection, in accordance with the constant-Stanton-number trend pointed out by Jones and Otis (1986). The range covered by the numerical experiments is 102 < Ra < 107, 0.71 < Pr < 100, and 0.25 < H/L < 1.

Experiments on mixing due to chaotic advection in a cavity

1989 ◽  
Vol 209 ◽  
pp. 463-499 ◽  
Author(s):  
C. W. Leong ◽  
J. M. Ottino
Keyword(s):  
Large Scale ◽  
Spatial Arrangement ◽  
Periodic Points ◽  
Chaotic Advection ◽  
Two Dimensional ◽  
Complex Behaviour ◽  
Chaotic Flows ◽  
Regular Time ◽  
Slow Flows ◽  
Time Periodic

Chaotic mixing of fluids in slow flows is ubiquitous but incompletely understood. However, relatively simple experiments provide a wealth of information regarding mixing mechanisms and indicate the need for complementary theoretical developments in dynamical systems. In this work we presnt a versatile cavity flow apparatus, capable of producing a variety of two-dimensional velocity fields, and use it to conduct a detailed experimental study of mixing in low-Reynolds-number flows. Since the goal is detailed understanding, only two time-periodic co-rotating flows induced by wall motions are considered: one continuous and the other discontinuous. Both types of flows produce exponential growth of intermaterial area, as expected from chaotic flows, and a mixture of islands and chaotic regions. A procedure for identifying periodic points and determining their movements is presented as well as how to make meaningful comparisons between periodic flows. We observe that periodic points move very much as a planetary system; planets (hyperbolic points) have moons (elliptic points) with twice the period of the planets; furthermore the spatial arrangement of periodic points becomes symmetric at regular time intervals. Detailed analyses reveal complex behaviour: birth, bifurcation, and collapse of islands; formation and periodic motion of coherent structures, such as islands and large-scale folds. However, the richness and complexity of the results obtained indicate that these two-dimensional time-periodic systems are far from completely understood and that other wall motions might deserve a similar level of scrutiny.

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