Generation of Large-Scale Winds in Horizontally Anisotropic Convection

We simulate three-dimensional, horizontally periodic Rayleigh-Bénard convection, confined between free-slip horizontal plates and rotating about a distant horizontal axis. When both the temperature difference between the plates and the rotation rate are sufficiently large, a strong horizontal wind is generated that is perpendicular to both the rotation vector and the gravity vector. The wind is turbulent, large-scale, and vertically sheared. Horizontal anisotropy, engendered here by rotation, appears necessary for such wind generation. Most of the kinetic energy of the flow resides in the wind, and the vertical turbulent heat flux is much lower on average than when there is no wind.

Figure 1

Instantaneous temperature fields in a vertical slice in the ($x,z$) plane at (a) $t=0.04$ and (b) $t=0.25$. The parameters are $R={10}^7$ and $2\mathrm{\Omega }={10}^4$, the top and bottom are free slip, and the rotation vector points into the page. Slices at other values of $y$ look qualitatively similar since the rotation makes variation in $y$ weak.

Figure 2

(a) Time series of volume-averaged specific kinetic energy in the direction of the wind $\frac{1}{2}⟨u^2⟩$, and normal to the wind $\frac{1}{2}⟨v^2+w^2⟩$; (b) vertical profiles of the wind velocity averaged horizontally and over 0.025 thermal times; (c) time series of the Nusselt numbers. An anticyclonic simulation (A) is started at time $t=0.25$ by applying the reflection $x\mapsto -x$ to the cyclonic simulation (C). The inset shows mean wind profiles, averaged horizontally and over $0.3\le t\le 0.75$; (d) vertical profiles of the temperature averaged horizontally and over 0.025 thermal times. The dots in panels (a) and (c) mark the starts of the time windows over which the profiles in panels (b) and (d) have been averaged.

Figure 3

(a) Vertical profiles of the wind velocity, averaged horizontally and over 0.4 thermal times; (b) ranges of $N(t)$ (mean, 5% and 95% percentiles, extreme values) explored by the experiments over 0.4 thermal times. Results for rotation rates of $2\mathrm{\Omega }=15\hspace{0.17em}000,8000,5000,3000,1000,0$ are shown for free-slip boundaries, along with results for $2\mathrm{\Omega }={10}^4$ with no-slip (NS) boundaries. Cyclonic (dashed lines) and anticyclonic (continuous lines) windy solutions result from different initial conditions.