We test the ability of a general low-dimensional model for turbulence to predict geometrydependent dynamics of large-scale coherent structures, such as convection rolls. The model consists of stochastic ordinary differential equations, which are derived as a function of boundary geometry from the Navier-Stokes equations [1,2]. We test the model using Rayleigh-Bénard convection experiments in a cubic container. The model predicts a new mode in which the alignment of a convection roll switches between diagonals. We observe this mode with a measured switching rate within 30% of the prediction.Large-scale coherent flow structures in turbulencesuch as convection rolls in the atmosphere -are ubiquitous and can play a dominant role in heat and mass transport. A particular challenge is to predict dynamical states and their change with different boundary geometries, for example in the way that local weather patterns depend on the topography of the Earth's surface. However, the Navier-Stokes equations that describe flows are impractically difficult to solve for turbulent flows, so lowdimensional models are desired.It has long been recognized that the dynamical states of large-scale coherent structures are similar to those of low-dimensional dynamical systems models [3] and stochastic ordinary differential equations [4][5][6][7]. However, such models tend to be descriptive rather than predictive, as parameters are typically fit to observations, rather than derived [8]. In particular, dynamical systems models tend to fail at quantitative predictions of new dynamical states in regimes outside where they were parameterized. In this letter we demonstrate a proof-of-principle that a general low dimensional model can quantitatively predict the different dynamical states of large-scale coherent structures in different geometries.The model system is Rayleigh-Bénard convection, in which a fluid is heated from below and cooled from above to generate buoyancy-driven convection [9,10]. This system exhibits robust large-scale coherent structures that retain the same organized flow structure over long times. For example, in upright cylindrical containers of aspect ratio 1, a large-scale circulation (LSC) forms. This LSC consists of temperature and velocity fluctuations which, when coarse-grain averaged, collectively form a single convection roll in a vertical plane [11], as shown in Fig. 1a. Various dynamics of the LSC have been reported, including spontaneous meandering of the orientation θ 0 in a horizontal plane, and an advected oscillation which appears as a torsional or sloshing mode [12][13][14][15][16][17][18]. As an example of different dynamical states in different geometries, if instead the axis of the cylinder is aligned horizontally, θ 0 tends to align with the longest diagonals of the cell, and oscillates periodically between diagonals and around individual corners [19]. While there are several low-dimensional models for LSC dynamics [20][21][22][23], only one by Brown & Ahlers has made predictions dependent on container ge...
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