ENGINEERING AND CFD

The characteristic patterns seen on the solar surface, on gas giants, in Earth's atmosphere and oceans, and many other geo- and astrophysical settings originate from turbulent convection dynamics flows driven by a density difference caused by, for instance, a temperature gradient. Convection in itself is inherently complex, but often it is the interaction with other forces, such as the Coriolis and Lorentz force due to rotation and magnetic fields, that determines the actual shape and behaviour of the flow structures. Understanding these convective patterns is often essentially tantamount to understanding the underlying physics at play. In this project, surveys through the huge parameter space are conducted, to not only categorise flow morphologies, but also to derive theoretical relations, in particular, for the heat and momentum transport.

Simulating the actual flow in the aforementioned systems is still far out of reach with current HPC systems and, moreover, many of the controlling parameters are not well-constrained. The approach followed in this project was to use simpler geometries such as cylinders and rectangular boxes that push the control parameters to the extreme and, indeed, close to realistic values. Carrying out suites of direct numerical simulations with varying material properties, thermal forcing and rotation rates, as well aspect ratios, in these basic configurations are an essential and necessary first step for gaining more insight into the far more complex geophysical and astrophysical flows. They enable more realistic and educated predictions and extrapolations. Due to its sheer vastness, however, exploring the possible parameter space requires supercomputing power.

One of the main questions addressed in this project was how the Prandtl number affects the flow. The Prandtl number is the ratio between viscosity and thermal diffusivity. Thus, often the Prandtl number is below unity like in Earth's core, the Sun, or gas planets, heat diffuses significantly more than momentum. This also poses severe demands on the numerical spatial and temporal resolution. On the other hand, the majority of laboratory experiments and also planetary dynamo simulations are carried out with moderate Prandtl numbers, being one and larger.

It was shown that thermally-driven convective flows in these low-Prandtl number flows are very different to moderate Prandtl number flows, specifically when the system is rotated. In the latter case, a special type of convection in the form of thermal inertial oscillating waves develops. The unique characteristic flow patterns were analysed by means of the dynamic mode decomposition that allows for extracting single modes and following their respective temporal evolutions.

Typical flow patterns occurring in rotating low Prandtl numbers fluids are shown in Figure 1. The flow is multi-modal with a broad range of different frequencies. In particular, also a torsional mode was observed, whose temporal evolution is presented in Figure 2. This type of mode has previously been argued to only occur in the presence of a magnetic field.

Research Team:

Olga Shishkina, Mohammad Emran, Xuan Zhang, Lukas Zwirner; Max Planck Institute for Dynamics and Self-Organization, Göttingen (Germany)
Susanne Horn; Earth, Planetary, and Space Sciences, University of California, Los Angeles (USA)

Publications:

Olga Shishkina, Susanne Horn, Mohammad Emran, Emily S. C. Ching. Mean temperature profiles in turbulent thermal convection. Phys. Rev. Fluids 2 (2017), 113502.
https://link.aps.org/doi/10.1103/PhysRevFluids.2.113502

Olga Shishkina. Mean flow structure in horizontal convection. J. Fluid Mech. 812 (2017), 525–540.
https://doi.org/10.1017/jfm.2016.866

Susanne Horn, Peter J. Schmid. Prograde, retrograde, and oscillatory modes in rotating Rayleigh–Bénard convection. J. Fluid Mech. 831 (2017), 182–211
https://doi.org/10.1017/jfm.2017.631

Olga Shishkina, Mohammad Emran, Siegfried Grossmann, Detlef Lohse. Scaling relations in large-Prandtl-number natural thermal convection. Phys. Rev. Fluids 2 (2017), 103502.
https://link.aps.org/doi/10.1103/PhysRevFluids.2.103502

Emily S. C. Ching, On-Yu Dung, Olga Shishkina. Fluctuating thermal boundary layers and heat transfer in turbulent Rayleigh–Bénard convection. J. Stat. Phys. 167 (2017), 626–635.
https://doi.org/10.1007/s10955-017-1739-5

Gijs L. Kooij, Mikhail A. Botchev, Edo M. A. Frederix, Bernard J. Geurts, Susanne Horn, Detlef Lohse, Erwin P. van der Poel, Olga Shishkina, Richard J.A.M. Stevens, Roberto Verzicco. Comparison of computational codes for direct numerical simulations of turbulent Rayleigh–Bénard convection. Computers & Fluids 166 (2018), 1–8.
https://www.sciencedirect.com/science/article/pii/S0045793018300100

Kai Leong Chong, Sebastian Wagner, Matthias Kaczorowski, Olga Shishkina, Ke-Qing Xia. Effect of Prandtl number on heat transport enhancement in Rayleigh–Bénard convection under geometrical confinement. Phys. Rev. Fluids 3 (2018), 013501.
https://journals.aps.org/prfluids/abstract/10.1103/PhysRevFluids.3.013501

Scientific Contact:

PD Dr. Olga Shishkina
Max Planck Institute for Dynamics and Self-Organization
Am Fassberg 17, D37077 Göttingen (Germany)
E-Mail: Olga.Shishkina[at]ds.mpg.de