Non-linear dynamics and pattern formation in a vertical fluid layer heated from the side

Bratsun, Dmitry; Zyuzgin, Alexej V; Putin, G. F.

doi:10.1016/s0142-727x(03)00086-9

Cited by 21 publications

(14 citation statements)

References 22 publications

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“…The first dimensionless group is the viscosity ratio: The second dimensionless group is the Grashof number: where ν d is the kinematic viscosity of the descending fluid ( μ d / ρ d ). The Grashof number compares viscous to buoyancy forces and it can indicate the transition between flow regimes in boundary layers and buoyancy‐driven flows [e.g., Jaluria , 2003; Jin and Chen , 1996; Bratsun et al , 2003]. Note that these two groups depend on the properties of the fluids and geometry of the conduit only.…”

Section: Magma Flow In Open Systemsmentioning

confidence: 99%

Constraints on the rates of degassing and convection in basaltic open-vent volcanoes

Palma

Blake

Calder

2011

Geochem. Geophys. Geosyst.

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[1] Variations in gas emissions of open-vent volcanoes are investigated using a model of magma convection in narrow conduits. Laboratory experiments with both vertical and inclined conduits and dimensional analysis show that for Grashof numbers lower than 100 the volumetric rate of magma ascent is a simple function of equivalent conduit radius, density difference between the magmas, and viscosity of the degassed magma that descends back to the reservoir. The rate of magma ascent depends on the flux coefficient, estimated as 0.1 and 0.2 for vertical and inclined conduits, respectively. The equivalent radius parameter accounts for the dimensions of the conduit(s) regardless of its geometry, thus extending the treatment by previous models that used flow in pipes. The volume flow rate of convection increases with higher density difference and conduit size, but is also highly influenced by the large variations in viscosity of the degassed magma as volatile content and crystallinity change. The model presented here can be used to constrain the degassing and ascent rates of volatile-rich magma when combined with petrologic data on magmatic volatile content. Application of the model to Villarrica volcano (Chile) reveals that the background degassing levels observed (∼3 kg s −1 SO 2 ) are associated with convective ascent of a relatively degassed magma (0.04 wt% S, ∼0.5 wt% H 2 O), while episodes of higher SO 2 emissions (measurements up to 15 kg s −1 ) can be explained by the ascent of magma with higher volatile content (up to 0.09 wt% S, ∼1.5 wt% H 2 O).

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Section: Magma Flow In Open Systemsmentioning

confidence: 99%

Constraints on the rates of degassing and convection in basaltic open-vent volcanoes

Palma

Blake

Calder

2011

Geochem. Geophys. Geosyst.

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“…However, their approach remains limited to a region around the critical Rayleigh number. Bratsun et al [27] carried out extensive experimental and numerical studies of the successive bifurcations of the flow in three dimensions, but their work was conducted at a high Prandtl number (Pr = 26) for which the primary instability consists of traveling waves. No equivalent study has been performed for air as far as we know.…”

Section: Introductionmentioning

confidence: 99%

Transition to chaos of natural convection between two infinite differentially heated vertical plates

et al. 2013

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Natural convection of air between two infinite vertical differentially heated plates is studied analytically in two dimensions (2D) and numerically in two and three dimensions (3D) for Rayleigh numbers Ra up to 3 times the critical value Ra(c)=5708. The first instability is a supercritical circle pitchfork bifurcation leading to steady 2D corotating rolls. A Ginzburg-Landau equation is derived analytically for the flow around this first bifurcation and compared with results from direct numerical simulation (DNS). In two dimensions, DNS shows that the rolls become unstable via a Hopf bifurcation. As Ra is further increased, the flow becomes quasiperiodic, and then temporally chaotic for a limited range of Rayleigh numbers, beyond which the flow returns to a steady state through a spatial modulation instability. In three dimensions, the rolls instead undergo another pitchfork bifurcation to 3D structures, which consist of transverse rolls connected by counter-rotating vorticity braids. The flow then becomes time dependent through a Hopf bifurcation, as exchanges of energy occur between the rolls and the braids. Chaotic behavior subsequently occurs through two competing mechanisms: a sequence of period-doubling bifurcations leading to intermittency or a spatial pattern modulation reminiscent of the Eckhaus instability.

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“…Errorbars are computed from the standard error of the Lyapunov exponent, assuming a Gaussian distribution for the evaluation of Eq. (6), and corresponding to a 95% confidence interval, i.e., with a half-width equal 1.96 times the standard error. We also note that sources of errors such as the distance to the attractor are not taken into account so that there may be some underestimation of the total error.…”

Section: B Period-doubling Cascadementioning

confidence: 99%

“…Bratsun et al [6] carried out extensive experimental and numerical studies of the successive bifurcations of the flow at the Prandtl number Pr = 26. The fluid layer was assumed to be of infinite vertical extent in the numerical simulations.…”

Section: Introductionmentioning

confidence: 99%

Chaotic dynamics of a convection roll in a highly confined, vertical, differentially heated fluid layer

et al. 2015

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Direct numerical simulation is used to study the air flow between two vertical plates maintained at different temperatures. The periodic dimensions of the plates are small so as to accommodate only one flow structure, which consists of a convection roll with oblique vorticity braids. At lower Rayleigh numbers, the roll and the braids grow and shrink alternatively following a cyclical process. As the Rayleigh number is increased, the flow becomes temporally chaotic through a period-doubling cascade. Windows corresponding to multiperiodic regimes and interior crises are observed. As the Rayleigh number is further increased, the structure intermittently switches between two vertical positions, which is seen to correspond to an "attractor-merging" crisis. The chaotic flow dynamics are characterized and the corresponding physical mechanisms are identified. We show that some of the flow key features, such as the chaotic oscillation and intermittency, can be captured by a low-order model.

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Non-linear dynamics and pattern formation in a vertical fluid layer heated from the side

Cited by 21 publications

References 22 publications

Constraints on the rates of degassing and convection in basaltic open-vent volcanoes

Constraints on the rates of degassing and convection in basaltic open-vent volcanoes

Transition to chaos of natural convection between two infinite differentially heated vertical plates

Chaotic dynamics of a convection roll in a highly confined, vertical, differentially heated fluid layer

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