scholarly journals Nonlinear Stability Problem of a Rotating Doubly Diffusive Porous Layer

1995 ◽  
Vol 190 (2) ◽  
pp. 373-390 ◽  
Author(s):  
J.L. Guo ◽  
P.N. Kaloni
Keyword(s):  
Porous Layer ◽  
Nonlinear Stability ◽  
Stability Problem

scholarly journals Nonlinear stability problem of a rotating porous layer

1995 ◽  
Vol 53 (1) ◽  
pp. 129-142 ◽  
Author(s):  
Y. Qin ◽  
P. N. Kaloni
Keyword(s):  
Porous Layer ◽  
Nonlinear Stability ◽  
Stability Problem

scholarly journals Optimal Stability Thresholds in Rotating Fully Anisotropic Porous Medium with LTNE

2021 ◽  
Author(s):  
Florinda Capone ◽  
Maurizio Gentile ◽  
Jacopo A. Gianfrani
Keyword(s):  
Porous Layer ◽  
Nonlinear Stability ◽  
Steady Motion ◽  
Vertical Axis ◽  
Linear Instability ◽  
List Type ◽  
Nonlinear Stability Analysis ◽  
Onset Of Convection ◽  
Anisotropic Porous Medium ◽  
Necessary And Sufficient

Abstract The onset of thermal convection in an anisotropic horizontal porous layer heated from below and rotating about vertical axis, under local thermal non-equilibrium hypothesis is studied. Linear and nonlinear stability analysis of the conduction solution is performed. Coincidence between the linear instability and the global nonlinear stability thresholds with respect to the L2—norm is proved. Article Highlights A necessary and sufficient condition for the onset of convection in a rotating anisotropic porous layer has been obtained. It has been proved that convection can occur only through a steady motion. A detailed proof is reported thoroughly. Numerical analysis shows that permeability promotes convection, while thermal conductivities and rotation stabilize conduction.

scholarly journals On the stability of carbon sequestration in an anisotropic horizontal porous layer with a first-order chemical reaction

2019 ◽  
Vol 475 (2226) ◽  
pp. 20180365 ◽  
Author(s):  
K. Gautam ◽  
P. A. L. Narayana
Keyword(s):  
Chemical Reaction ◽  
Porous Layer ◽  
Nonlinear Stability ◽  
Anisotropy Ratio ◽  
Neutral Stability ◽  
First Order ◽  
Order Chemical Reaction ◽  
Linear And Nonlinear ◽  
First Order Chemical Reaction ◽  
The Stability

Carbon dioxide (CO 2 ) sequestration in deep saline aquifers is considered to be one of the most promising solutions to reduce the amount of greenhouse gases in the atmosphere. As the concentration of dissolved CO 2 increases in unsaturated brine, the density increases and the system may ultimately become unstable, and it may initiate convection. In this article, we study the stability of convection in an anisotropic horizontal porous layer, where the solute is assumed to decay via a first-order chemical reaction. We perform linear and nonlinear stability analyses based on the steady-state concentration field to assess neutral stability curves as a function of the anisotropy ratio, Damköhler number and Rayleigh number. We show that anisotropy in permeability and solutal diffusivity play an important role in convective instability. It is shown that when solutal horizontal diffusivity is larger than the vertical diffusivity, varying the ratio of vertical to horizontal permeabilities does not significantly affect the behaviour of instability. It is also noted that, when horizontal permeability is higher than the vertical permeability, varying the ratio of vertical to horizontal solutal diffusivity does have a substantial effect on the instability of the system when the reaction rate is dominated by the diffusion rate. We used the Chebyshev-tau method coupled with the QZ algorithm to solve the eigenvalue problem obtained from both the linear and nonlinear stability theories.

scholarly journals On the Effects of Circulation around a Circle on the Stability of a Thomson Vortex N-gon

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 1033
Author(s):  
Leonid Kurakin ◽  
Irina Ostrovskaya
Keyword(s):  
Circular Cylinder ◽  
Hamiltonian Systems ◽  
Nonlinear Stability ◽  
Vortex Dynamics ◽  
Stability Problem ◽  
Orbital Stability ◽  
Stability And Instability ◽  
The Stability ◽  
Parameter Values ◽  
Linear Setting

The stability problem of the stationary rotation of N identical point vortices is considered. The vortices are located on a circle of radius R 0 at the vertices of a regular N-gon outside a circle of radius R. The circulation Γ around the circle is arbitrary. The problem has three parameters N, q, Γ , where q = R 2 / R 0 2 . This old problem of vortex dynamics is posed by Havelock (1931) and is a generalization of the Kelvin problem (1878) on the stability of a regular vortex polygon (Thomson N-gon) on the plane. In the case of Γ = 0 , the problem has already been solved: in the linear setting by Havelock, and in the nonlinear setting in the series of our papers. The contribution of this work to the solution of the problem consists in the analysis of the case of non-zero circulation Γ ≠ 0 . The linearization matrix and the quadratic part of the Hamiltonian are studied for all possible parameter values. Conditions for orbital stability and instability in the nonlinear setting are found. The parameter areas are specified where linear stability occurs and nonlinear analysis is required. The nonlinear stability theory of equilibria of Hamiltonian systems in resonant cases is applied. Two resonances that lead to instability in the nonlinear setting are found and investigated, although stability occurs in the linear approximation. All the results obtained are consistent with those known for Γ = 0 . This research is a necessary step in solving similar problems for the case of a moving circular cylinder, a model of vortices inside an annulus, and others.

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