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We establish a nonlinear energy stability theory for the problem of convection in a porous medium when the viscosity depends on the temperature. This is, in fact, the situation which is true in real life and has many applications to geophysics. The nonlinear analysis presented here would appear to require the presence of a Brinkman term in the momentum equation, rather than just the normal form of Darcy's law.
We study the influence of natural convection on stability of reaction fronts in
porous media. The model consists of the heat equation, of the equation for the depth of
conversion and of the equations of motion under the Darcy law. Linear stability analysis of
the problem is fulfilled, the stability boundary is found. Direct numerical simulations are
performed and compared with the linear stability analysis.
Propagation of polymerization fronts with liquid monomer and liquid polymer is considered
and the influence of vibrations on critical conditions of convective instability is
studied. The model includes the heat equation, the equation for the concentration and the
Navier-Stokes equations considered under the Boussinesq approximation. Linear stability
analysis of the problem is fulfilled, and the convective instability boundary is found
depending on...
The aim of this paper is to study the effect of vibrations on convective instability of
reaction fronts in porous media. The model contains reaction-diffusion equations coupled
with the Darcy equation. Linear stability analysis is carried out and the convective
instability boundary is found. The results are compared with direct numerical
simulations.
This paper considers the effect of a perturbed wall in regard to the classical Benard convection problem in which the lower rigid surface is of the form , s=ε r, in axisymmetric cylindrical polar coordinates (r,ϕ,z). The boundary conditions at s=0 for the linear amplitude equation are found and it is shown that these conditions are different from those which apply to the nonlinear problem investigated by Brown and Stewartson [1], representing the distribution of convection cells near the center....
Nous prouvons que pour toute solution du problème de Kelvin–Helmholtz des nappes de tourbillons pour l’équation d’Euler bi-dimensionnelle, définie localement en temps, la courbe de saut de et la densité de tourbillon sont analytiques (sous une hypothèse de régularité Holderienne de la courbe de saut). Nous donnons également un résultat de régularité partielle de la trace de sur lorsque est définie sur un demi-interval .
Nous prouvons que pour toute solution u du problème
de Kelvin–Helmholtz des nappes de tourbillons pour
l'équation d'Euler bi-dimensionnelle, définie localement en
temps,
la courbe de saut de u et la densité de tourbillon sont
analytiques (sous une hypothèse de régularité Holderienne
de la courbe de saut).
Nous donnons également un résultat de régularité partielle
de la trace de u sur t=0 lorsque u est définie sur un
demi-interval [O,T[.
The Lyapunov direct method is applied to study nonlinear exponential stability of a basic motionless state to imposed linear temperature and concentration fields of a binary fluid mixture heated and salted from below, in the Oberbeck-Boussinesq scheme. Stress-free and rigid surfaces are considered and absence of Hopf bifurcation is assumed. We prove the coincidence of the linear and (unconditional) nonlinear critical stability limits, when the ratio between the Schmidt and the Prandtl numbers is...
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