Double-diffusive convection with two stabilizing gradients: strange consequences of magnetic buoyancy

1995 ◽  
Vol 301 ◽  
pp. 383-406 ◽  
Author(s):  
D. W. Hughes ◽  
N. O. Weiss
Keyword(s):  
Magnetic Field ◽  
Active Regions ◽  
Finite Amplitude ◽  
Thermosolutal Convection ◽  
Horizontal Magnetic Field ◽  
Magnetic Diffusivity ◽  
Diffusive Convection ◽  
Mean Pressure ◽  
Magnetic Buoyancy ◽  
Double Diffusive

Instabilities due to a vertically stratified horizontal magnetic field (magnetic buoyancy instabilities) are believed to play a key role in the escape of the Sun's internal magnetic field and the formation of active regions and sunspots. In a star the magnetic diffusivity is much smaller than the thermal diffusivity and magnetic buoyancy instabilities are double-diffusive in character. We have studied the nonlinear development of these instabilities, in an idealized two-dimensional model, by exploiting a non-trivial transformation between the governing equations of magnetic buoyancy and those of classical thermosolutal convection. Our main result is extremely surprising. We have demonstrated the existence of finite-amplitude steady convection when both the influential gradients (magnetic and convective) are stabilizing. This strange behaviour is caused by the appearance of narrow magnetic boundary layers, which distort the mean pressure gradient so as to produce a convectively unstable stratification.

Double-diffusive Magnetic Layering

2021 ◽  
Vol 922 (2) ◽  
pp. 195
Author(s):  
D. W. Hughes ◽  
N. H. Brummell
Keyword(s):  
Magnetic Field ◽  
Chemical Elements ◽  
Turbulent Transport ◽  
Linear Instability ◽  
Thermosolutal Convection ◽  
Horizontal Magnetic Field ◽  
Diffusive Regime ◽  
Magnetic Buoyancy ◽  
Double Diffusive

Abstract Double-diffusive systems, such as thermosolutal convection, in which the density depends on two components that diffuse at different rates, are prone to both steady and oscillatory instabilities. Such systems can evolve into layered states, in which both components, and also the density, adopt a “staircase” profile. Turbulent transport is enhanced significantly in the layered state. Here we exploit an analogy between magnetic buoyancy and thermosolutal convection in order to demonstrate the phenomenon of magnetic layering. We examine the long-term nonlinear evolution of a vertically stratified horizontal magnetic field in the so-called “diffusive regime,” where an oscillatory linear instability operates. Motivated astrophysically, we consider the case where the viscous and magnetic diffusivities are much smaller than the thermal diffusivity. We demonstrate that diffusive layering can occur even for subadiabatic temperature gradients. Magnetic layering may be relevant for stellar radiative zones, with implications for the turbulent transport of heat, magnetic field, and chemical elements.

On the Chaotic Dynamics Associated with the Center Manifold Equations of Double-Diffusive Convection Near a Codimension-Four Bifurcation Point at Moderate Thermal Rayleigh Number

2018 ◽  
Vol 28 (08) ◽  
pp. 1850094 ◽  
Author(s):  
Justin Eilertsen ◽  
Jerry Magnan
Keyword(s):  
Bifurcation Point ◽  
Center Manifold ◽  
Poincaré Map ◽  
Three Dimensional ◽  
Thermosolutal Convection ◽  
Poincare Map ◽  
Lorenz Equations ◽  
Frequency Locking ◽  
Diffusive Convection ◽  
Double Diffusive

We analyze the dynamics of the Poincaré map associated with the center manifold equations of double-diffusive thermosolutal convection near a codimension-four bifurcation point when the values of the thermal and solute Rayleigh numbers, [Formula: see text] and [Formula: see text], are comparable. We find that the bifurcation sequence of the Poincaré map is analogous to that of the (continuous) Lorenz equations. Chaotic solutions are found, and the emergence of strange attractors is shown to occur via three different routes: (1) a discrete Lorenz-like attractor of the three-dimensional Poincaré map of the four-dimensional center manifold equations that forms as the result of a quasi-periodic homoclinic explosion; (2) chaos that follows quasi-periodic intermittency occurring near saddle-node bifurcations of tori; and, (3) chaos that emerges from the destruction of a 2-torus, preceded by frequency locking.

The Influence of Coupled Molecular Diffusion on Double-Diffusive Convection in a Porous Medium

1986 ◽  
Vol 108 (4) ◽  
pp. 872-876 ◽  
Author(s):  
N. Rudraiah ◽  
M. S. Malashetty
Keyword(s):  
Porous Medium ◽  
Molecular Diffusion ◽  
Normal Mode Analysis ◽  
Finite Amplitude ◽  
Mode Analysis ◽  
Double Diffusive Convection ◽  
Amplitude Analysis ◽  
Cross Diffusion ◽  
Diffusive Convection ◽  
Double Diffusive

The effect of coupled molecular diffusion on double-diffusive convection in a horizontal porous medium is studied using linear and nonlinear stability analyses. In the case of linear theory, normal mode analysis is employed incorporating two cross diffusion terms. It is found that salt fingers can form by taking cross-diffusion terms of appropriate sign and magnitude even when both concentrations are stably stratified. The conditions for the diffusive instability are compared with those for the formation of fingers. It is shown that these two types of instability will never occur together. The finite amplitude analysis is used to derive the condition for the maintenance of fingers. The stability boundaries are drawn for three different combinations of stratification and the effect of permeability is depicted.

scholarly journals Magneto Convection in a Layer of Nanofluid With Soret Effect

2015 ◽  
Vol 9 (2) ◽  
pp. 63-69 ◽  
Author(s):  
Ramesh Chand ◽  
Gian Chand Rana
Keyword(s):  
Magnetic Field ◽  
Rayleigh Number ◽  
Volume Fraction ◽  
Fluid Layer ◽  
Soret Effect ◽  
Lewis Number ◽  
Horizontal Layer ◽  
Diffusive Convection ◽  
Mode Method ◽  
Double Diffusive

AbstractDouble diffusive convection in a horizontal layer of nanofluid in the presence of uniform vertical magnetic field with Soret effect is investigated for more realistic boundary conditions. The flux of volume fraction of nanoparticles is taken to be zero on the isothermal boundaries. The normal mode method is used to find linear stability analysis for the fluid layer. Oscillatory convection is ruled out because of the absence of the two opposing buoyancy forces. Graphs have been plotted to find the effects of various parameters on the stationary convection and it is found that magnetic field, solutal Rayleigh number and nanofluid Lewis number stabilizes fluid layer, while Soret effect, Lewis number, modified diffusivity ratio and nanoparticle Rayleigh number destabilize the fluid layer.

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