Pressure-potential-temperature covariance in convection with rotation

The pressure-potential-temperature covariance in free and rotating turbulen t convection with no mean velocity shear is analysed, using a dataset gener ated with a large-eddy simulation (LES) model. The pressure field is resolv ed into turbulence-turbulence, buoyancy and Coriolis components, and the co ntributions from these components to the pressure-gradient-potential-temper ature covariance in the budget equation for the potential-temperature flux are examined. In non-rotating convection, the buoyancy contribution compensates for about one half of the buoyant production term in the flux budget equation, and t he turbulence-turbulence contribution is well approximated by the Rotta-typ e return-to-isotropy model with the relaxation time-scale set proportional to the turbulence energy dissipation time-scale. In convection with rotation, neither the simplest Rotta-type model with the relaxation time-scale proportional to the energy dissipation time-scale no r the more sophisticated two-component-limit (TCL) nonlinear model are able to accurately describe the LES data. A somewhat better agreement is found when a limitation is imposed on the relaxation time-scale due to the backgr ound rotation. The simplest model for the buoyancy contribution, where it i s set proportional to the buoyant production term in the flux budget equati on, fares poorly. The TCL model shows better agreement with LES data althou gh some uncertainties remain. However, the relative importance of the buoya ncy contribution to the pressure-gradient-potential-temperature covariance decreases with increasing rotation rate. In contrast, the Coriolis contribution becomes more important as the rotati on rate increases. Neither the simplest linear model for the Coriolis contr ibution nor the much more complex nonlinear TCL model are found to be adequ ate. Neither model appropriately accounts for the component of the angular velocity of rotation that is parallel to the component of the pressure grad ient in question. In the seemingly simplest case considered in the present paper, when the rotation vector is aligned with the vector of gravity, no C oriolis contribution to the vertical-pressure-gradient-potential-temperatur e covariance is predicted by these models. This results in a strong underes timation of the pressure term in the flux budget equation and may lead to a n erroneous prediction of the vertical potential-temperature flux in convec tion with rotation. In an attempt to remedy the situation, an extension of the TCL model that contains only one extra empirical coefficient is develop ed and checked against LES data.