M.C. Navarro

Instabilities in buoyant flows under localized heating

We study, from the numerical point of view, instabilities developed in a fluid layer with a free surface in a cylindrical container which is nonhomogeneously heated from below. In particular, we consider the case in which the applied heat is localized around the origin. An axisymmetric basic state appears as soon as a nonzero horizontal temperature gradient is imposed. The basic state may bifurcate to different solutions depending on vertical and lateral temperature gradients and on the shape of the heating function. We find different kinds of instabilities: extended patterns growing on the whole domain, which include those known as targets, and spiral waves. Spirals are present even for infinite Prandtl number. Localized structures both at the origin and at the outer part of the cylinder may appear either as Hopf or stationary bifurcations. An overview of the developed instabilities as functions of the dimensionless parameters is presented in this article.

Evolution of secondary whirls in thermoconvective vortices: Strengthening, weakening, and disappearance in the route to chaos.

The appearance, evolution, and disappearance of periodic and quasiperiodic dynamics of fluid flows in a cylindrical annulus locally heated from below are analyzed using nonlinear simulations. The results reveal a route of the transition from a steady axisymmetric vertical vortex to a chaotic flow. The chaotic flow regime is reached after a sequence of successive supercritical Hopf bifurcations to periodic, quasiperiodic, and chaotic flow regimes. A scenario similar to the Ruelle-Takens-Newhouse scenario is verified in this convective flow. In the transition to chaos we find the appearance of subvortices embedded in the primary axisymmetric vortex, flows where the subvortical structure strengthens and weakens, that almost disappears before reforming again, leading to a more disorganized flow to a final chaotic regime. Results are remarkable as they connect to observations describing formation, weakening, and virtual disappearance before revival of subvortices in some atmospheric swirls such as dust devils.

Thermoconvective vortices in a cylindrical annulus with varying inner radius

This paper shows the influence of the inner radius on the stability and intensity of vertical vortices, qualitatively similar to dust devils and cyclones, generated in a cylindrical annulus non-homogeneously heated from below. Little relation is found between the intensity of the vortex and the magnitude of the inner radius. Strong stable vortices can be found for both small and large values of the inner radius. The Rankine combined vortex structure, that characterizes the tangential velocity in dust devils, is clearly observed when small values of the inner radius and large values of the ratio between the horizontal and vertical temperature differences are considered. A contraction on the radius of maximum azimuthal velocity is observed when the vortex is intensified by thermal mechanisms. This radius becomes then nearly stationary when frictional force balances the radial inflow generated by the pressure drop in the center, despite the vortex keeps intensifying. These results connect with the behavior of the radius of the maximum tangential wind associated with a hurricane.

Instabilities due to a heating spike

We study numerically instabilities developed in a fluid layer with a free surface, in a cylindrical container which around the origin at the bottom has a heating spike modelled by a parameter β. Axysimmetric basic states appear as soon a non-zero horizontal temperature gradient is imposed. These states are characterized by the presence of a hot boundary layer in the center and a convective motion in the whole cell. The basic states may bifurcate to different solutions depending on the parameters of the problem. We consider the small aspect ratio and high localization case. Waves (spirals) or stationary patterns with low wave numbers appear after the bifurcation. They are more localized depending on the localization of the heating.

Computational Aspects of a Time Evolution Scheme for Incompressible Boussinesq Navier-Stokes in a Cylinder

In this work we show some computational aspects of the implementation of a three dimensional spectral time evolution scheme for incompressible Boussinesq Navier-Stokes including rotation effects in a cylinder with a primitive variable formulation. The scheme is a second-order time-splitting method combined with pseudo-spectral Fourier Chebyshev in space. To deal with the singularity at the origin a radial expansion is considered in the diameter of the cylinder. The order expansion in the radial coordinate gets doubled. We develop a matrix processing that combines the use of the parity of the fields and the discretization functions to cancel half of the terms in the matrix reducing the radial dimension to the original one.