Rotating Convection

In typical experiments of rotating Rayleigh–Bénard convection the fluid is confined in a cylinder and rotated about its vertical axis. Thus, to allow for a comparison with the experimental setup at the MPI-DS we employ the same geometry in our direct numerical simulations. Although the setup is rather simple, the generated turbulent flows are highly complex and provide physical insight into the rotating buoyancy-driven flows occurring in geo- and astrophysics.

Instantaneous temperature fields of a fluid with Pr=0.8 and Ra=10⁸; the rotation rate increases from left to right, with the leftmost being still.

In our recent work Xuan, et al., Phys. Rev. Lett. 124 (2020), experiments and direct numerical simulations reveal a boundary zonal flow (BZF) that replaces the classical large-scale circulation in rapidly rotating turbulent convection. The BZF is located near the vertical side wall and enables enhanced heat transport there. While the azimuthal velocity of the BZF is cyclonic (in the rotating frame), the temperature is an anticyclonic traveling wave of mode one whose signature is a bimodal temperature distribution. With increasing rotation (decreasing Ekman number Ek) the BZF width shrinks as ~ Ek^2/3. Together with experiements, BZF is confirmed existing at very high Ra and over wide range of Ra with extened scaling ~ Ra^1/4Ek^2/3.

For Ra=109, 1/Ro = 10, Pr = 0.8, D/H = 1/2. (a, b) angle-time plots at r=r0 (where time-averaged azimuthal velocity is zero, same radial location as indicated by solid circle in (c,d)), z=H/2 (a) T and (b) uz; (c) normalized time-averaged vertical heat flux; (d) instantaneous vertical vorticity. Adopted from Xuan, et al., Phys. Rev. Lett. 124 (2020) — For Ra=10⁹, 1/Ro = 10, Pr = 0.8, D/H = 1/2. (a, b) angle-time plots at r=r₀ (where time-averaged azimuthal velocity is zero, same radial location as indicated by solid circle in (c,d)), z=H/2 (a) T and (b) u_z; (c) normalized time-averaged vertical heat flux; (d) instantaneous vertical vorticity. Adopted from Xuan, *et al., Phys. Rev. Lett.* **124** (2020)

For Ra=10⁹, 1/Ro = 10, Pr = 0.8, D/H = 1/2. (a, b) angle-time plots at r=r₀ (where time-averaged azimuthal velocity is zero, same radial location as indicated by solid circle in (c,d)), z=H/2 (a) T and (b) u_z; (c) normalized time-averaged vertical heat flux; (d) instantaneous vertical vorticity. Adopted from Xuan, *et al., Phys. Rev. Lett.* **124** (2020)

Video 1

Video 2

Short-time averaged (averaged every 10 free-fall time units) vorticity field (Video 1) and temperature field (Video 2) at z=H/2, Pr = 0.8, D/H = 1/2, Ra=10⁹, 1/Ro = 10 (fast rotation case). Near the sidewall small cyclonic vortices are formed and are located nicely around the BZF circle, while temperature field drifts anticyclonically.

Xuan Zhang, Dennis P. M. van Gils, Susanne Horn, Marcel Wedi, Lukas Zwirner, Guenter Ahlers, Robert E. Ecke, Stephan Weiss, Eberhard Bodenschatz, Olga Shishkina. Boundary Zonal Flow in rotating turbulent Rayleigh-Bénard convection. Phys. Rev. Lett. 124 (2020), 084505.

Susanne Horn and Olga Shishkina. Toroidal and poloidal energy in rotating Rayleigh–Bénard convection. J. Fluid Mech. 762 (2015), 232–255.

Susanne Horn and Olga Shishkina. Rotating non-Oberbeck–Boussinesq Rayleigh–Bénard convection in water. Phys. Fluids 26 (2014), 055111.

Rotating Convection

Further reading