The hockey-stick transition (HOST) about the turbulence kinetic energy with the averaged flow intensity is wildly noticed in the nocturnal boundary layer, which is explained by the ‘local and global shear’ assumption. However, the intrinsic mechanism about averaged flow effected on turbulence kinetic energy via shear and buoyancy is missing. In this research article, we deploy the Koopman operator to expose invariant subspaces of the Ri series to identify the quasi-periodic coherent structures from the single tower observation. Analysis of turbulence fluxes and anisotropy demonstrates horizontal kinetic energy with vertical downward flux coupled mechanism changes anisotropy evolution. Examining the anisotropy invariants changing with kinetic energy revealed a dynamical transition that determines the threshold of HOST. Moreover, the mechanism about how the shear and vertical momentum influences the transition point of HOST is firstly given by a group of a quadratic relationship when the anisotropy crossed over the transition point.