Asymptotic methods based on those of geometrical optics are applied to some steady convection-diffusion streamed flows at a high Péclet number. Even with the assumption of inviscid, irrotational flow past a body with uniform ambient conditions, the rays from which the solution is constructed can only be found after local analyses have been carried out near the stagnation points. In simple cases...

Whereas penumbral models during the last 15 years have been successful in explaining Evershed flows and magnetic field inclination variations in terms of flux tubes, the lack of contact between these models and a convective process needed to explain the penumbral radiative heat flux has been disturbing. We report on recent observational and theoretical evidence that challenge flux tube interpre...

This paper is divided in two parts. In the first part, a brief review of a spectral element method for the numerical solution of the incompressible Navier-Stokes equations is given. The method is then extended to compute buoyant flows described by the Boussinesq approximation. Free convection in closed two-dimensional cavities are computed and the results are in very good agreement with the ava...

A new technique is used to explore the structure of turbulent convecting flows. A sinusoidal temperature perturbation is superimposed on the bottom plate of a cylindrical convection cell filled with cryogenic helium gas and its decay is measured at the cell mid-height. The measurements allow the first dynamic estimate of the core part of the flow which conducts fluid effectively without any the...

We review here various recent applications of Wassertein–type metrics to both nonlinear partial differential equations and integro–differential equations. Among others, we can describe the asymptotic behavior of nonlinear friction equations arising in the kinetic modelling of granular flows, and the growth of the support in nonlinear diffusion equations of porous medium type. Further examples i...

The Boussinesq equations for Rayleigh–Bénard convection are simulated for a cylindrical container with an aspect ratio near 1.5. The transition from an axisymmetric stationary flow to time-dependent flows is studied using nonlinear simulations, linear stability analysis and bifurcation theory. At a Rayleigh number near 25 000, the axisymmetric flow becomes unstable to standing or travelling azi...

The instability of convection rolls in a fluid layer heatet from below is studied in the case where the layer rotates about an axis slightly inclined with respect to the vertical. The inclination destroys the horizontal isotropy of the layer, but the instability of rolls found by Küppers and Lortz [1] is little affected as long as the angle of inclination is small. A new effect is the generatio...