Vertical turbulence structure and second‐moment budgets in convection with rotation: A large‐eddy simulation study

Abstract

AbstractThe structure of the instantaneous flow fields and turbulence statistics and the second‐order moment budgets in convection affected by rotation are analysed using a large‐eddy simulation (LES) dataset. Three archetypes of convective flows driven by the surface buoyancy flux are generated. One is the reference case of the non‐rotating convective boundary layer (CBL) growing into a quiescent stably stratified fluid. The other two are CBLs affected by rotation. In the geophysical turbulence context, these non‐rotating and rotating CBLs mimic an early stage and a mature stage, respectively, of the vertical mixing phase of open‐ocean deep convection.Instantaneous flow structures reveal strong localization of the buoyancy anomalies and the n on‐hydrostatic pressure anomalies near the surface in rotating CBLs and their dilution as one moves towards the CBL outer edge. These anomalies are associated with the localized cyclonic vortices which are the centres of intense vertical motions. Most of the cyclones never reach the outer edge of the CBL.Increasing rotation results in less mixing, reducing the entrapment flux at the CBL outer edge and maintaining a negative buoyancy gradient throughout the CBL. The effect of counter‐gradient transport, which occurs in free convection, is largely reduced. The vertical‐velocity variance and the layer‐averaged turbulence kinetic energy are reduced by rotation, while the variances of buoyancy and pressure are enhanced. The vertical velocity and buoyancy fields are positively skewed in both rotating and free convection. The buoyancy skewness is considerably larger in the bulk of the rotating CBL than in the non‐rotating CBL, reflecting strong localization of positive buoyancy anomalies.The pressure transport term in the turbulence kinetic‐energy budget becomes more important as the rotation rate increases, whereas the contribution of the third‐order transport term is reduced. All terms in the buoyancy variance budget grow in amplitude as the rotation rate increases. The mean‐gradient term and the turbulent transport term are both gains that are offset by a loss to dissipation in the bulk of the CBL. This is different from free convection where the buoyancy variance budget in mid CBL is maintained mainly by turbulent transport since the mean‐gradient term is small there. The budget of the vertical buoyancy flux in convection with rotation is strongly dominated by the pressure‐gradient/buoyancy covariance and the buoyancy production terms.Evaluation of closures for the turbulence energy dissipation against the LES data supports the idea of imposing a limitation on the dissipation length scale due to the background rotation. This limitation is required to account for the reduced turbulence energy in convection with rotation. A similar limitation on the length scale for the dissipation of buoyancy variance is not found to be important. Analysis of parametrized budgets of the third‐order moments reveals the dominance of the direct effects of buoyancy. These effects are enhanced with increasing rotation rate. They must be included in parametrizations for the third‐order moments. The conventional down‐gradient approximations neglecting the buoyancy effects would greatly underestimate the turbulent transport.