1,923 research outputs found
Asymmetric magnetic reconnection with a flow shear and applications to the magnetopause
We perform a theoretical and numerical study of anti-parallel 2D magnetic
reconnection with asymmetries in the density and reconnecting magnetic field
strength in addition to a bulk flow shear across the reconnection site in the
plane of the reconnecting fields, which commonly occurs at planetary
magnetospheres. We predict the speed at which an isolated X-line is convected
by the flow, the reconnection rate, and the critical flow speed at which
reconnection no longer takes place for arbitrary reconnecting magnetic field
strengths, densities, and upstream flow speeds, and confirm the results with
two-fluid numerical simulations. The predictions and simulation results counter
the prevailing model of reconnection at Earth's dayside magnetopause which says
reconnection occurs with a stationary X-line for sub-Alfvenic magnetosheath
flow, reconnection occurs but the X-line convects for magnetosheath flows
between the Alfven speed and double the Alfven speed, and reconnection does not
occur for magnetosheath flows greater than double the Alfven speed. We find
that X-line motion is governed by momentum conservation from the upstream
flows, which are weighted differently in asymmetric systems, so the X-line
convects for generic conditions including sub-Alfvenic upstream speeds. For the
reconnection rate, while the cutoff condition for symmetric reconnection is
that the difference in flows on the two sides of the reconnection site is twice
the Alfven speed, we find asymmetries cause the cutoff speed for asymmetric
reconnection to be higher than twice the asymmetric form of the Alfven speed.
The results compare favorably with an observation of reconnection at Earth's
polar cusps during a period of northward interplanetary magnetic field, where
reconnection occurs despite the magnetosheath flow speed being more than twice
the magnetosheath Alfven speed, the previously proposed suppression condition.Comment: 46 pages, 7 figures, abstract abridged here, accepted to Journal of
Geophysical Research - Space Physic
Convective Fingering of an Autocatalytic Reaction Front
We report experimental observations of the convection-driven fingering
instability of an iodate-arsenous acid chemical reaction front. The front
propagated upward in a vertical slab; the thickness of the slab was varied to
control the degree of instability. We observed the onset and subsequent
nonlinear evolution of the fingers, which were made visible by a {\it p}H
indicator. We measured the spacing of the fingers during their initial stages
and compared this to the wavelength of the fastest growing linear mode
predicted by the stability analysis of Huang {\it et. al.} [{\it Phys. Rev. E},
{\bf 48}, 4378 (1993), and unpublished]. We find agreement with the thickness
dependence predicted by the theory.Comment: 11 pages, RevTex with 3 eps figures. To be published in Phys Rev E,
[email protected], [email protected], [email protected]
Modification of the eikonal relation for chemical waves to include fluid flow
Propagating wave fronts resulting from autocatalytic chemical reactions have been the focus of much recent research. For the most part, the hydrodynamics resulting from such reactions has been neglected. In this work, a relation is derived for the normal speed of a propagating wave front as a function of the local curvature when fluid motion is allowed. This āāeikonalāā equation is a generalization of one which was derived in the absence of fluid flow. It is also shown that small variations in the fluid density due to the chemical reaction do not change the form of the relation
Finite Thermal Diffusivity at Onset of Convection in Autocatalytic Systems: Discontinuous Fluid Density
A linear convective stability analysis for propagating autocatalytic reaction fronts includes density differences due to both thermal and chemical gradients. Critical parameters for the onset of convection are calculated for an unbounded geometry, a vertical slab, and a vertical cylinder. Thermal effects are important at unstable wavelengths well above the critical wavelength for the onset of convection
Hydrodynamic Instability of Chemical Waves
We present a theory for the transition to convection for flat chemical wave fronts propagating upward. The theory is based on the hydrodynamic equations and the oneāvariable reactionādiffusion equation that describes the chemical front for the iodateāarsenous acid reaction. The reaction term involves the reaction rate constants and the chemical composition of the mixture. This allows the discussion of the effects of the different chemical variables on the transition to convection. We have studied perturbations of different wavelengths on an unbounded flat chemical front and found that for wavelengths larger than a critical wavelength (Ī»ā³Ī»c) the perturbations grow in time, while for smaller wavelengths the perturbations diminish. The critical wavelength depends not only on the density difference between the unreacted and reacted fluids, but also on the speed and thickness of the chemical front
Nonlinear Front Evolution of Hydrodynamic Chemical Waves in Vertical Cylinders
The nonlinear stability of three-dimensional reaction-diffusion fronts in vertical cylinders is considered using the viscous hydrodynamic fluid equations in the limit of infinite thermal diffusivity. A nonlinear front evolution equation is presented and used to examine the transition from nonaxisymmetric to axisymmetric convection observed in experiments performed in cylinders. Comparisons with experiments show excellent agreement in both the shape and speed of the front
Convective Turing Patterns
Turing patterns involve regions of different chemical compositions which lead to density gradients that, in liquids, are potentially unstable hydrodynamically. Nonlinear hydrodynamics coupled with a model of Turing pattern formation show that convection modifies and coexists with some Turing patterns and excludes others, and thereby plays a significant role in pattern selection
Convective Chemical-wave Propagation in the Belousov- Zhabotinsky Reaction
We investigate the onset of convection for chemical-wave propagation in the Belousov-Zhabotinsky reaction based on the two-variable Oregonator model coupled with the fluid dynamic equations. For chemical waves in a vertical slab, two-dimensional convection occurs only for slab widths greater than a critical threshold width. The convective threshold is different for ascending and descending waves. Convectionless waves are flat and propagate with constant speed. Above the onset of convection, the wave velocity increases and the flat wave deforms due to two counterrotating steady rolls. For a horizontal slab, convection is always present and the wave velocity increases with increasing slab width. Our results are compared with experiments
Transitions Between Convective Patterns in Chemical Fronts
We present a theory for the transition from nonaxisymmetric to axisymmetric convection in iodate-arsenous acid reaction fronts propagating in a vertical slab. The transition takes place away from the onset of convection, where a convectionless flat front becomes unstable to a nonaxisymmetric convective front. The transition is studied by numerically solving a reaction-diffusion equation coupled with nonlinear hydrodynamics in a two-dimensional slab
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