Liang Wei
Geert Brethouwer
Philipp Schlatter
Arne V. Johansson
Linné FLOW Centre,
KTH Mechanics
Stockholm, Sweden

Snapshot from a numerical experiment of turbulent flow between two parallel plates rotating spanwise. The image shows strong turbulence (hairpin-like structures with one or two legs) near the lower wall and little turbulence but large, rolling waves (dark blue) near the upper wall.

Many fluid flows in industry and nature involve turbulence with system rotation, such as flows in quickly rotating gas turbines and pumps, ocean currents, and the atmosphere. As a potentially more canonical example, we study the fully turbulent flow between two parallel plates – so-called plane turbulent channel flow – with rotation along the spanwise direction (plate width direction). We employ direct numerical simulation (DNS) to virtually realize the flow in a computer, using up to 10 billion grid points and 4,096 processors to compute the evolution of the flow over time. It is well known that system rotation usually enhances the turbulence close to one wall, and dampens fluctuations close to the other. If the flow rate (measured by the Reynolds number) is high enough, very interesting and unexpected phenomena start to appear.

In the picture, an instantaneous snapshot shows strong fine-scale turbulent vortices (light blue) near the lower wall. Meanwhile, large-scale spanwise-oriented rollers (dark blue) – so-called Tollmien-Schlichting (TS) waves – are seen to develop near the upper wall. Characteristic hairpin-like vortices (red represents high local flow velocity) densely populate the interface between the turbulent lower and quieter upper sides of the channel. Over time, the TS waves grow and get stronger, but as they get stronger they become more unstable and eventually break down into intense small-scale turbulence. This turbulence on the originally quiet channel side then quickly decays, leading to the formation of TS waves again. This cyclical process is embedded in the turbulent dynamics.

This work is supported by the Swedish Research Council (VR). SNIC (Swedish National Infrastructure for Computing), the Knut and Alice Wallenberg (KAW) Foundation and PRACE (Partnership for Advanced Computing in Europe) are acknowledged for providing computing time.

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