# Convective turbulence

Starting with my PhD thesis, and continued thereafter, I have studied some canonical turbulent systems through direct numerical simulations: Taylor-Couette flow, Rayleigh-Bénard convection and Double diffusive convection.

These systems are used as basic models when trying to understand the behaviour of more complicated natural or man-made flows. For example, Rayleigh-Bénard is useful to understand what is happening inside the Earth's mantle, why the oceanic currents behave like they do, or how is heat transported inside the sun. Likewise, Taylor-Couette can be used as a basic model for many shear flows, going from the astrophysical scale -accretion disks around protostars- to the flow around a jetski's hull. Double diffusive convection is commonly used to model the convection in the ocean. So even if these are easy systems to construct and simulate, they find applicability in many places and not all is known about them. Because my research has focused on several aspects of these systems, the following description is divided into three subsections.

## Transitions, scaling laws and boundary layers

My PhD thesis mainly focused on investigating the boundary layer transitions in the Taylor-Couette system, and its relation to the analogous Rayleigh-Bénard problem. The main idea was to determine the relationship between driving, either in the form of cylinder shear, or temperature-difference, to the response, in the shape of either torque, or total heat transported, and to write scaling laws which related them. These would be different depending on which "regime" the flow was in, i.e. whether the boundary layers were turbulent, how strong rotation is and other factors. While I think that this problem is now better for basic Taylor-Couette, and we have a better idea of how the boundary layers behave, depending on rotation, there are still many interesting questions to solve for these paradigmatic flows. For very strong rotation, Rayleigh-Bénard enters the so-called geostrophic regime, dominated by Coriolis forces. This is the regime most relevant to the atmosphere, and simulations are barely starting to scratch the surface.

## Large-scale (super) structures and their manipulation

Another question I'm still interested in is on the nature of the large scale structures which form, c.f. the Taylor rolls in this video. Even for very large Reynolds numbers, and in very large computational boxes, these structures seem to be pinned in the same location over time. Up to now, the mechanisms behind this stationarity are not really well understood. Investigating them could lead to the posibility of manipulating their position over time, a research question with interesting practical consequences for industry and geo-physics. During the last few years, we have tried different ways of manipulating or modelling these structures, by playing around with boundary conditions, introducing sudden rotation, or letting them decay, with varying degrees of success in advancing understanding. This understanding will lead to more insight on geophysical flows, as is described in this article or this other article on how the continents affect the convection in the mantle.

## The effect of moisture

Interestingly enough, structures seem to form in similar ways in non-rotating Rayleigh-Bénard and Taylor-Couette. However, structures for rotating Rayleigh-Bénard look completely different, and look like the cylone/anti-cyclone patterns find in Earth's weather, these would require very different sorts of manipulations if one would want to control their position. However, having a basic model of a hurricane is a complicated problem, as phase transitions play a crucial role. So it is not enough to have rotation, one would need to incorporate phase changes too. A question I would like to address is how to do this effectively.

## Relevant articles

### Transitions, scaling laws and boundary layers

- Boundary layer dynamics at the transition between the classical and the ultimate regime of Taylor-Couette flow.
**R. Ostilla Mónico, E. P. van der Poel, R. Verzicco, S. Grossmann, D. Lohse***Physics of Fluids, 26, 015114 (2014)*. [arxiv] [PoF] - Exploring the phase diagram of fully turbulent Taylor-Couette flow.
**R. Ostilla Mónico, E. P. van der Poel, R. Verzicco, S. Grossmann, D. Lohse***Journal of Fluid Mechanics, 761, 1-26 (2014)*. [arxiv] [jfm] - Logaritmic mean temperature profiles and their connection to plume emissions in Turbulent Rayleigh-Bénard convection.
**E. P. van der Poel, R. Ostilla Mónico, R. Verzicco, S. Grossmann, D. Lohse***Physical Review Letters, 115, 154501*. [PRL] [arxiv] - The near-wall region of highly turbulent Taylor-Couette flow.
**R. Ostilla Mónico, R. Verzicco, S. Grossmann, D. Lohse***Journal of Fluid Mechanics, 768, 95-117, (2016)*. [jfm] [arxiv] - Geostrophic convective turbulence: The effect of boundary layers.
**R. P. J. Kunnen, R. Ostilla Mónico, E. P. van der Poel, R. Verzicco, D. Lohse***Journal of Fluid Mechanics, 799, 413-432 (2016)*. [arxiv] [jfm]

### Large-scale structures and their manipulation

- Effects of the computational domain size on DNS of Taylor-Couette turbulence with stationary outer cylinder.
**R. Ostilla Mónico, R. Verzicco, D. Lohse***Physics of Fluids, 27, 025110 (2015)*. [arxiv] [PoF] - Turbulent Taylor-Couette flow with stationary inner cylinder.
**R. Ostilla Mónico, R. Verzicco, D. Lohse***Journal of Fluid Mechanics, 799, R1 (2016)*. [arxiv] [jfm] - Mixed insulating and conducting thermal boundary conditions in Rayleigh-Bénard convection.
**Dennis Bakhuis, Rodolfo Ostilla-Mónico, Erwin P. van der Poel, Roberto Verzicco, Detlef Lohse***J. Fluid Mech., 835, 491-511 (2018)*[JFM - OpenAccess] [arXiv] - Mixed thermal conditions in convection: how do continents affect the mantle's circulation?
**R. Ostilla-Mónico***J. Fluid Mech. Focus on Fluids, 822, 1-4, (2017).*[JFM - Open Access]