Cyclonic and anticyclonic rotation in a cylinder cooled inhomogeneously on the top

In this work, we study the development of vortical structures generated in a rotating cylinder non-homogeneously cooled on the top. In the axisymmetric regime, for moderate vertical temperature differences and any rotation rate, cyclonic and anticyclonic rotations coexist in the flow: a counterclockwise motion at upper levels, giving place to a vertical top-down vortex, and a clockwise rotation at lower levels that generates a spin up motion. For lower rotation rates and high enough vertical temperature differences, only cyclonic top-down vortices survive and get stronger. We perform a force balance analysis to explain the phenomena. In the non-axisymmetric regime, no anticyclonic rotation at the bottom is reported and the cyclonic top-down vortex either disappears or splits up in two top-down vortices, depending on the ambient rotation rate. The intensity of the cooling on the top and how localized this cool region is affect the flow developed. When the horizontal temperature difference on the top is larger than the vertical temperature difference between top and bottom, stable axisymmetric top-down vortices with an inner updraft of warmer air are reported. The more localized the cooling above, the more difficult the development of the inner updraft becomes. Results may contribute to the understanding of the relevance of thermal processes in tornadogenesis.

Generation of a magnetic field by a double vortex in a rotating cylinder

In this paper we use simulations of the magnetohydrodynamic equations coupled with heat to show the generation of magnetic field by the dynamical interaction of a pair of vortices in a fluid electrically conducting within a cylindrical domain nonhomogeneously heated from below, setting in a rotation frame. For large enough rotation rates we show that the formation of a pair of vortices inside the primary whirl gives rise to a magnetic field. The magnetic field has a strong horizontal component, and the magnetic lines go from one vortex to the other.

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.

Top-down vortices developed in a cylindrical annulus cooled on the top

In this paper we study the generation of top-down vortices by thermoconvective mechanisms in a cylindrical annulus nonhomogeneously cooled on the top. Assuming axisymmetry we study the structure of the vortices, characterized by a spiral downward motion, similar to that observed in tornadoes generated in supercell storms.

Model of lymphoma from stochastic analysis

In this work, the authors introduce a stochastic model of lymphoma. Two clonotypes of T cells of the immune system compete with each other and with other clonotypes for survival stimuli. One of the clonotypes is normal and the other is tumourous. To model the tumourous clonotype the authors include a rate of influx of new naive T cells (descendants of mutated precursor cells) from the thymus. The authors obtain a deterministic approximation to the stochastic model and analyse eight cases of competition between the two clonotypes of T cells. The authors obtain two possible scenarios, depending on the values of parameters: either both clonotypes survive in the repertoire or the clonotype of the normal T cells becomes extinct, meanwhile the clonotype of the tumourous T cells is maintained, after achieving some maximum level of growth. The authors show that if the income of the new tumourous T cells from the thymus is augmented, then the tumourous clonotype, would never be removed from the repertoire; meanwhile the normal clonotype could become extinct if it was not specialised enough to compete effectively for survival stimuli provided by professional cells.

Effects of thermal gradients on the intensity of vortices generated in a cylindrical annulus

This paper shows the influence of horizontal and vertical temperature gradients on the intensity of vertical vortices, qualitatively similar to dust devils, generated by a convective instability in a cylindrical annulus non-homogeneously heated. The behavior of the vortices formed is studied, showing that the increase of the temperature gradients intensifies the strength of the vortical structures developed and vice versa, small horizontal and vertical temperature gradients lead to weaker vortices or even make them disappear. Consequently, the intensity of the vortices can be controlled thermally by cooling or heating adequately the bottom boundary.

Vortices in a cylindrical annulus nonhomogeneously heated: effect of localized heating on their stability and intensity

In this paper we study the influence of localized or widespread nonhomogeneous temperature profiles on the stability and intensity of vertical vortices generated in a cylindrical annulus by a convective instability. Localized profiles lead to more stable vortices while widespread inhomogeneities intensify the spin motion around the inner cylinder.

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.

Effects of optimal control over thermoconvective patterns

This paper shows that optimal control techniques can be used to avoid some pattern formation in a Rayleigh-Bénard problem with horizontal temperature gradient. Appropriate thermal boundary conditions determined by these techniques lead to new strong controlled basic states with reduced pattern and for which the thermoconvective instability is avoided.

Bifurcation diversity of dynamic thermocapillary liquid layers

We study, from the theoretical point of view, instabilities appearing in a liquid layer, where a dynamic flow is imposed through a nonzero temperature gradient at the bottom. Experimentally many interesting dynamical behaviors have been discovered in this system. In this Brief Report we prove that the basic solution can display great richness of bifurcations which are controlled by heat related parameters. Different kinds of spatially extended and localized structures appear, which are both stationary or oscillatory. These last ones can present amazing patterns such as squares or spirals. Also competing solutions at codimension-two bifurcation points have been found: stationary radial rolls with different wave numbers, radial rolls with hydrothermal waves, and hydrothermal waves with different wave numbers. Remarkably our results recover many features of numerous reported experiments, predict new instabilities, and by giving a deeper insight into how physical parameters contribute to bifurcations, open a gateway to control those instabilities.