491 research outputs found
Double-diffusive instabilities of a shear-generated magnetic layer
Previous theoretical work has speculated about the existence of
double-diffusive magnetic buoyancy instabilities of a dynamically evolving
horizontal magnetic layer generated by the interaction of forced vertically
sheared velocity and a background vertical magnetic field. Here we confirm
numerically that if the ratio of the magnetic to thermal diffusivities is
sufficiently low then such instabilities can indeed exist, even for high
Richardson number shear flows. Magnetic buoyancy may therefore occur via this
mechanism for parameters that are likely to be relevant to the solar
tachocline, where regular magnetic buoyancy instabilities are unlikely.Comment: Submitted to ApJ
Singular diffusionless limits of double-diffusive instabilities in magnetohydrodynamics
We study local instabilities of a differentially rotating viscous flow of
electrically conducting incompressible fluid subject to an external azimuthal
magnetic field. In the presence of the magnetic field the hydrodynamically
stable flow can demonstrate non - axisymmetric azimuthal magnetorotational
instability (AMRI) both in the diffusionless case and in the double-diffusive
case with viscous and ohmic dissipation. Performing stability analysis of
amplitude transport equations of short-wavelength approximation, we find that
the threshold of the diffusionless AMRI via the Hamilton-Hopf bifurcation is a
singular limit of the thresholds of the viscous and resistive AMRI
corresponding to the dissipative Hopf bifurcation and manifests itself as the
Whitney umbrella singular point. A smooth transition between the two types of
instabilities is possible only if the magnetic Prandtl number is equal to
unity, . At a fixed the threshold of the
double-diffusive AMRI is displaced by finite distance in the parameter space
with respect to the diffusionless case even in the zero dissipation limit. The
complete neutral stability surface contains three Whitney umbrella singular
points and two mutually orthogonal intervals of self-intersection. At these
singularities the double-diffusive system reduces to a marginally stable system
which is either Hamiltonian or parity-time (PT) symmetric.Comment: 34 pages, 8 figures, typos corrected, refs adde
Theoretical and numerical investigation of diffusive instabilities in multi-component alloys
Mechanical properties of engineering alloys are strongly correlated to their
microstructural length scale. Diffusive insta- bilities of the Mullins-Sekerka
type is one of the principal mechanisms through which the scale of the
microstructural features are determined during solidification. In contrast to
binary systems, in multicomponent alloys with arbitrary interdiffusivities, the
growth rate as well as the maximally growing wavelengths characterizing these
instabilities depend on the the dynamically selected equilibrium tie-lines and
the steady state growth velocity. In this study, we derive analytical
expressions to characterize the dispersion behavior in isothermally solidified
multicomponent (quaternary) alloys for different choices of the
inter-diffusivity matrices and confirm our calculations using phase-field
simulations. Thereafter, we perform controlled studies to capture and isolate
the dependence of instability length scales on solute diffusivities and steady
state planar front velocities, which leads to an understanding of the process
of length scale selection during the onset of instability for any alloy
composition with arbitrary diffusivities, comprising of both independent and
coupled diffusion of solutes.Comment: 17 pages, 9 figure
Symmetry breaking in a bulk-surface reaction-diffusion model for signaling networks
Signaling molecules play an important role for many cellular functions. We
investigate here a general system of two membrane reaction-diffusion equations
coupled to a diffusion equation inside the cell by a Robin-type boundary
condition and a flux term in the membrane equations. A specific model of this
form was recently proposed by the authors for the GTPase cycle in cells. We
investigate here a putative role of diffusive instabilities in cell
polarization. By a linearized stability analysis we identify two different
mechanisms. The first resembles a classical Turing instability for the membrane
subsystem and requires (unrealistically) large differences in the lateral
diffusion of activator and substrate. The second possibility on the other hand
is induced by the difference in cytosolic and lateral diffusion and appears
much more realistic. We complement our theoretical analysis by numerical
simulations that confirm the new stability mechanism and allow to investigate
the evolution beyond the regime where the linearization applies.Comment: 21 pages, 6 figure
Double-Diffusive Convection
Much progress has recently been made in understanding and quantifying
vertical mixing induced by double-diffusive instabilities such as fingering
convection (usually called thermohaline convection) and oscillatory
double-diffusive convection (a process closely related to semiconvection). This
was prompted in parts by advances in supercomputing, which allow us to run
Direct Numerical Simulations of these processes at parameter values approaching
those relevant in stellar interiors, and in parts by recent theoretical
developments in oceanography where such instabilities also occur. In this paper
I summarize these recent findings, and propose new mixing parametrizations for
both processes that can easily be implemented in stellar evolution codes.Comment: To be published in the proceedings of the conference "New Advances in
Stellar Physics: from microscopic to macroscopic processes", Roscoff, 27-31st
May 201
A Weak Nonlinear Stability Analysis of Double Diffusive Convection with Cross-diffusion in a Fluid-saturated Porous Medium
he effect of “Cross Diffusion” on the linear and nonlinear stability of double diffusive convection in a fluid-saturated porous medium has been studied analytically. In the case of linear theory, the normal mode technique has been used and the condition for the maintenance of “finger” and “diffusive” instabilities have been obtained. It has been found that fingers can form by taking cross diffusion terms of appropriate sign and magnitude even though both components make stabilizing contributions to the net vertical density gradient. It has also been shown that “finger” and “diffusive” instabilities can never occur simultaneously. The nonlinear theory is based on the truncated representation of Fourier series and it has been found that the finite amplitude convection may occur when both initial property gradients are stabilizing. Further, the region of finite amplitude instability always encloses the region of infinitesimal oscillatory instability. The effects of permeability and cross-diffusion terms on the heat and mass transports have also been clearly brought out
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