Parameterization sensitivity and instability characteristics of the maximum sustainable heat flux framework for predicting turbulent collapse

Abstract

A maximum sustainable heat flux (MSHF) framework for the collapse of turbulence in the stable boundary layer has been previously studied using a one-dimensional model of Couette flow with parameterized turbulent fluxes. This study further investigates the stability properties of this model and assesses the robustness of the MSHF framework for predicting turbulent collapse to the choice of turbulence parameterization. The dynamic stability properties of the system are studied through numerical analysis of linearized equations of motion, and these results are compared with numerical solutions of the fully nonlinear system. While the MSHF mechanism and the qualitative features of the equilibrium structure are robust to changes in turbulence parameterizations, important quantitative differences between the models are found. While the equilibrium structures for Businger-Dyer-type stability functions are independent of the roughness length z0, all of the other relations show a strong dependence on z0 with regard to their shapes and the value of the MSHF. Equilibrium curves for some of the parameterizations exhibit multiple extrema, and transitions between stable and unstable regimes occur at extrema of the equilibrium curves in parameter space. Along the unstable branch(es), the Couette flow model has only a single unstable mode for all turbulence parameterizations considered. The MSHF framework is qualitatively robust to the choice of parameterization, but its use to predict the collapse of turbulence in the SBL is quantitatively sensitive to the turbulence scheme, especially for small values of z0.