Rotating Turbulent Convection

Rotating turbulent convection Rotation with thermally induced buoyancy governs many astrophysical and geophysical processes in the atmosphere, ocean, sun, and Earth’s liquid-metal outer core. Rotating Rayleigh–Bénard convection (RRBC) occurs in a fluid that fills a container with heated bottom and cooled top and rotated about its vertical axis with a constant angular velocity. RRBC is an extremely rich system, with features directly comparable to geophysical and astrophysical phenomena.

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 one of our former studies 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) 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.

In one of our recent studies R. E. Ecke and O. Shishkina, Annu. Rev. Fluid Mech. 55, 603 (2023), a unifying heat transport scaling approach for the transition between rotation-dominated (RD) and buoyancy-dominated (BD) regimes in RRBC was proposed and validated.
In R. E. Ecke, X. Zhang, and O. Shishkina, Phys. Rev. Fluids 7, L011501 (2022), X. Zhang, P. Reiter, O. Shishkina and R. E. Ecke, Phys. Rev. Fluids 9, 053501 (2024), RRBC was studied using DNS in cylindrical cells for broad ranges of Ra,Γ and rotation rates (inverse Ekman number Ek). We connected linear wall-mode states that occur prior to the onset of bulk convection with the boundary zonal flow (BZF) that coexists with turbulent bulk convection in the geostrophic regime. The results confirmed that wall modes are strongly linked with the BZF being the robust remnant of nonlinear wall mode states. In J. Song, O. Shishkina and X. Zhu, J. Fluid Mech. 989, A3 (2024), J. Song, V. Kannan, O. Shishkina and X. Zhu, Int. J. Heat Mass Transfer 232, 125971 (2024), the DNS of RRBC in the planar geometry with no-slip top and bottom and periodic lateral boundaries were performed for Ra up to 5×1013 and Ek down to 5×10−9. With increasing Ra, the DNS has revealed not only the typical RD regimes, namely, cellular flow, Taylor columns, plumes, geostrophic turbulence and large-scale vortices, but also the BD regime.