Critical flux Richardson number for Kolmogorov turbulence enabled by TKE transport

In stably stratified flows, the flux Richardson number Ri _f is a measure of the ratio between buoyancy destruction and shear production of turbulent kinetic energy (TKE). In flows with local equilibrium between shear production, buoyancy destruction and dissipation of TKE, the critical Ri _f,c≈0.21 corresponds to the limit above which Kolmogorov turbulence can no longer be sustained. Analysis of the TKE and velocity variance budget equations shows that the critical Ri _f,c is increased by the presence of positive turbulent transport of TKE. This situation is observed, for example, in the roughness sublayer above plant canopies, as demonstrated using field data from the Amazon rainforest.