In questo lavoro si studia la instabilità gravitazionale di un fluido comprimibile, elettroconduttore, descritto dalle equazioni della magnetofluidodinamica in presenza delle correnti di Hall e di ion slip. Si determina la condizione per la instabilità relativa ad una classe di perturbazioni assialsimmetriche.
The Rayleigh-Bénard convection for a couple-stress fluid with a thermorheological effect in the presence of an applied magnetic field is studied using both linear and non-linear stability analysis. This problem discusses the three important mechanisms that control the onset of convection; namely, suspended particles, an applied magnetic field, and variable viscosity. It is found that the thermorheological parameter, the couple-stress parameter, and the Chandrasekhar number influence the onset of...
The stability and evolution of very thin, single component, metallic-melt films is studied by analysis of coupled strongly nonlinear equations for gas-melt (GM) and crystal-melt (CM) interfaces, derived using the lubrication approximation. The crystal-melt interface is deformable by freezing and melting, and there is a thermal gradient applied across the film. Linear analysis reveals that there is a maximum applied far-field temperature in the gas, beyond which there is no film instability. Instabilities...
This article presents a survey of a new dynamical systems theory for 2D incompressible flows and its applications to geophysical fluid dynamics.
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...
We derive a very sharp nonlinear stability result for the problem of thermal convection in a layer of dielectric fluid subject to an alternating current (AC). It is particularly important to note that the size of the initial energy in which we establish global nonlinear stability is not restricted whatsoever, and the Rayleigh-Roberts number boundary coincides with that found by a formal linear instability analysis.