Periodic Reporting for period 4 - TROCONVEX (Turbulent Rotating Convection to the Extreme)
Período documentado: 2020-10-01 hasta 2021-09-30
Many large-scale flows in nature are thermally driven and subsequently shaped due to rotation of the planet or star on which these flows exist. Examples abound: Earth’s atmosphere and oceans, its liquid-metal interior (the so-called outer core), the interior of the giant gas planets in our solar system; even the outer layer of our Sun is flowing largely according to these basic forces. The effects of rotation are not intuitive: it is, for example, the reason why low-pressure areas on the northern hemisphere always rotate counterclockwise and high-pressure areas clockwise, a result of the dominant so-called geostrophic force balance between pressure gradient and Coriolis force. In deeper layers than the rather shallow atmosphere rotation generally leads to an organisation of the flow into columnar whirls or vortices aligned with the rotation axis. Researchers have found that this classical picture, taken mostly from relatively small-scale laboratory experiments, changes when looking at the limit of very large rotating systems (think of planets and stars). Instead, a new state called “geostrophic turbulence” is found, the properties of which are not quite known yet.
We want to explore this new state with a unique custom-designed experiment and with cutting-edge computer simulations. One of the most important aspects to know is the amount of heat that can be transported through a layer of gas or liquid. This is a major contribution to any energy budget model for these natural flows. We can directly measure the heat transport in our large experiment, a rotating cylinder with a height of up to 4 m, filled with water, heated from below and cooled from above. By the sheer size of this experiment we can access the new geostrophic turbulence state better than any other previous effort. The numerical simulations provide additional information: we can look at every detail of the flow. This step is also carried out in the experiment, though we can only see the flow in a small cross-section of the entire cylinder. Still, this will be enough to compare results from experiment and simulation..
The results will bring a better understanding of the natural flows mentioned above. We will give valuable input to get a grip on the origin and generation of Earth’s magnetic field, that is formed in the outer core and shields us from harmful radiation from space. We get to know more about the interior of the giant gas planets and the Sun. Additionally, these results may also contribute to climate modelling.
The main conclusions at the end of the project are several. We have gained an understanding of the various flow features observed in rapidly rotating convection by identifying the principal forces (e.g. inertia, Coriolis force, viscous effects). We have reproduced these flow features in great detail in the experiment. One surprising result is the generation of a so-called wall mode, a strong and persistent circulatory flow near the sidewall, that is quite decisive for the overall flow behaviour. The wall mode has been studied in detail, though its effect on the bulk flow is not yet completely clear. Another major finding is the formation of large-scale domain-filling vortex structures, both in simulations and in experiments, a sign of upscale transfer of energy contrary to the usual energy transfer down the spatial scales. A significant step towards true extrapolation to large-scale flows has been set, although new questions (like the wall mode) have popped up along the way.
We want to explore this new state with a unique custom-designed experiment and with cutting-edge computer simulations. One of the most important aspects to know is the amount of heat that can be transported through a layer of gas or liquid. This is a major contribution to any energy budget model for these natural flows. We can directly measure the heat transport in our large experiment, a rotating cylinder with a height of up to 4 m, filled with water, heated from below and cooled from above. By the sheer size of this experiment we can access the new geostrophic turbulence state better than any other previous effort. The numerical simulations provide additional information: we can look at every detail of the flow. This step is also carried out in the experiment, though we can only see the flow in a small cross-section of the entire cylinder. Still, this will be enough to compare results from experiment and simulation..
The results will bring a better understanding of the natural flows mentioned above. We will give valuable input to get a grip on the origin and generation of Earth’s magnetic field, that is formed in the outer core and shields us from harmful radiation from space. We get to know more about the interior of the giant gas planets and the Sun. Additionally, these results may also contribute to climate modelling.
The main conclusions at the end of the project are several. We have gained an understanding of the various flow features observed in rapidly rotating convection by identifying the principal forces (e.g. inertia, Coriolis force, viscous effects). We have reproduced these flow features in great detail in the experiment. One surprising result is the generation of a so-called wall mode, a strong and persistent circulatory flow near the sidewall, that is quite decisive for the overall flow behaviour. The wall mode has been studied in detail, though its effect on the bulk flow is not yet completely clear. Another major finding is the formation of large-scale domain-filling vortex structures, both in simulations and in experiments, a sign of upscale transfer of energy contrary to the usual energy transfer down the spatial scales. A significant step towards true extrapolation to large-scale flows has been set, although new questions (like the wall mode) have popped up along the way.
The main progress on the experimental side of the research is the completion of the experimental setup (a picture is enclosed). It is now the tallest rotating convection experiment in the world, with an unprecedented range of experiment conditions to consider. Every single experiment may last anywhere from one to four days. The most interesting experiments take the longest; they are at conditions for which rotation is truly dominant in the flow and buoyant energy input is rather low. We have also made sure to benchmark the setup by comparing to earlier heat transfer measurements for convection without rotation and a very good agreement is reached. These temperature and heat transfer measurements have allowed us to identify various subranges in the geostrophic regime, states with specific flow structures and corresponding scaling of the heat transfer. The wall mode has given an unexpected contribution, but has turned out to be an interesting feature for investigation. It is important to understand the effects of the wall mode for accurate interpretation of experimental results (which obviously require a sidewall) in the context of geo-/astrophysical systems (generally without lateral bounds).
The results from the experiments are further elucidated by accompanying numerical simulations. Two types of simulations have been performed. We use cylindrical domains to study the wall mode, with perfect agreement with the experiments. We also consider horizontally periodic domains to mimic the unbounded natural flows. In these simulations we have additionally considered different working fluids. The most interesting observation is the formation of a large-scale vortex in convection of a fluid with a high thermal conductivity, like a liquid metal. The large-scale vortex has thus far only been observed in computations with artificial stress-free boundary conditions; here it is observed for realistic no-slip boundary conditions as in the experiment. Such vortices could be the flow structures causing swirling, helical currents in the Earth’s liquid-metal outer core that generate Earth’s magnetic field. Additionally, we have substantiated the identification of the various subranges and corresponding flow structures by a careful consideration of the force balance in the flow. The dominant force balance is the geostrophic balance between Coriolis force and pressure gradient; the subdominant force balance dictates which flow features are formed.
Next to the heat transfer measurements we have been performing optical flow measurement inside the cylinder. A new transparent section has been designed that can be put in place of one of the other cylinder sections. We have been able to collect flow statistics at more extreme conditions than ever before. A remarkable large-scale vortex organization with four vortices is observed. There is an intricate interplay with the wall mode.
The results from the experiments are further elucidated by accompanying numerical simulations. Two types of simulations have been performed. We use cylindrical domains to study the wall mode, with perfect agreement with the experiments. We also consider horizontally periodic domains to mimic the unbounded natural flows. In these simulations we have additionally considered different working fluids. The most interesting observation is the formation of a large-scale vortex in convection of a fluid with a high thermal conductivity, like a liquid metal. The large-scale vortex has thus far only been observed in computations with artificial stress-free boundary conditions; here it is observed for realistic no-slip boundary conditions as in the experiment. Such vortices could be the flow structures causing swirling, helical currents in the Earth’s liquid-metal outer core that generate Earth’s magnetic field. Additionally, we have substantiated the identification of the various subranges and corresponding flow structures by a careful consideration of the force balance in the flow. The dominant force balance is the geostrophic balance between Coriolis force and pressure gradient; the subdominant force balance dictates which flow features are formed.
Next to the heat transfer measurements we have been performing optical flow measurement inside the cylinder. A new transparent section has been designed that can be put in place of one of the other cylinder sections. We have been able to collect flow statistics at more extreme conditions than ever before. A remarkable large-scale vortex organization with four vortices is observed. There is an intricate interplay with the wall mode.
The focal point of the project is the realisation and employment of a unique experimental setup that we use to dive deeper into the regime of rapidly rotating convection. This apparatus goes beyond the state of the art; results obtained in this project are treading new ground.
At the same time, we have performed numerical simulations to get detailed information on many aspects of this flow that are not directly available from the experiment. We have also pushed beyond the state of the art by employing large-scale parallel simulations on supercomputers. These computations have provided new insights, such as the unexpected wall mode near the sidewall with an intricate flow behaviour as well as a consistent explanation of the succession of flow states in subranges of the geostrophic regime using the balance of forces in the flow. A key finding is the formation of large-scale vortices in domains with experimentally realisable boundary conditions.
At the same time, we have performed numerical simulations to get detailed information on many aspects of this flow that are not directly available from the experiment. We have also pushed beyond the state of the art by employing large-scale parallel simulations on supercomputers. These computations have provided new insights, such as the unexpected wall mode near the sidewall with an intricate flow behaviour as well as a consistent explanation of the succession of flow states in subranges of the geostrophic regime using the balance of forces in the flow. A key finding is the formation of large-scale vortices in domains with experimentally realisable boundary conditions.