Abstract/Summary

Atmospheric convection is hugely important for weather and climate prediction, but parametrizations of the process in weather and climate models often behave poorly. Traditional parametrization assumptions break down at resolutions comparable to the dominant energy-containing structures. Lack of understanding of this convective “grey zone” is one of the biggest barriers to improving our representation of convection. The grey zone is a concept that applies to any turbulent flow — dry or moist. Therefore this thesis focuses on the simplest convection problem: Rayleigh-B´enard convection (RBC). It is shown that RBC possesses remarkably similar grey zone behaviour to that observed in numerical weather prediction models. In convection, large portions of the turbulent fluxes are carried by coherent structures. This motivates the split into “convection” and “environment” underlying traditional mass flux schemes, which can be generalized via conditional filtering. Introducing explicit discontinuous fluid relabelling terms leads to a multi-fluid equation set that is more complete than those currently published. New expressions for resolved relabelling terms are derived, and an argument is presented linking pressure differences between fluids to an isotropic stress introduced by relabelling. To show the validity of the multi-fluid approach, a 1D, time-dependent model of RBC is developed. The model has one rising and one falling fluid, and assumes that this split captures all subfilter variability. A scaling argument for the pressure differences between fluids reduces the free parameters to two O(1) constants. After determining these constants, correct scalings of the domain-averaged heat and momentum fluxes are predicted over six decades of buoyancy forcing. Thus even a simple two-fluid model can capture the essentials of convection. In 2D, the same model formulation improves initiation of convection across the grey zone, and reduces sensitivity of heat and momentum fluxes to grid spacing, compared to a single-fluid model with constant viscosity. It is shown that the closures successful in a single column do not provide sufficient constraint to maintain the correct sign of vertical velocity in the grey zone. The need for better understanding of the relabelling terms and their resolution-dependence emerges as the key barrier to progress.