Rotating convection with centrifugal buoyancy: Numerical predictions for laboratory experiments

In Coriolis-centrifugal convection (C3), buoyancy effects not only drive convective motions in the vertical direction due to the gravitational acceleration but also in the radial direction due to the centrifugal acceleration [Horn and Aurnou, Phys. Rev. Lett. 120, 204502 (2018)PRLTAO0031-900710.1103/PhysRevLett.120.204502]. Here, we use the flexibility of numerical simulations to vary the gravitational Rossby number Ro¥ and the rotational Froude number Fr independently and thereby study C3 over the broadest available parameter space. Based on our simulation results we give predictions for laboratory experiments of rotating convection, which inevitably include centrifugal effects. We especially focus on the spatial distribution of the temperature field. Unlike idealized Coriolis convection in which centrifugal buoyancy is neglected, the vertical temperature profiles become strongly radially dependent and exhibit a top-bottom asymmetry with increasing Froude number. In the quasicyclostrophic regime the temperature in the center of the fluid volume shows a strong enhancement, reaching values close to the bottom boundary temperature, whereas the temperatures at the sidewall are well below the arithmetic mean. We find further that the axisymmetric, linear model of Hart and Ohlsen [Phys. Fluids 11, 2101 (1999)PHFLE61070-663110.1063/1.870072] cannot be used to accurately predict the measured center temperatures, and provide an alternative empirical function based on our fully three-dimensional simulation results. Suggestions are given for the optimal local thermal measurement positions in laboratory experiments to estimate the global heat transfer and the vertical mean-temperature profiles in centrifugally affected rotating convection cases.