The influence of turbulence memory associated with curved trajectories: A pseudo-second-order closure for near-surface turbulence and an application to idealized tornadoes

Abstract:

The eddy-viscosity closure employed by turbulence parameterization schemes in atmospheric models assumes that the unresolved shear stress is directed opposite the resolved shear. This assumption ignores the physics that turbulent motions are generated and dissipated at finite rates – in effect, turbulence has a memory through its lifetime. In this work, a theoretical derivation from the evolution equation of the kinematic stress tensor shows that when an air parcel moves along a curved trajectory, a normal surface-shear-stress component arises owing to turbulence memory. A pseudo-second-order closure for near-surface turbulence is proposed to account for the effect of turbulence memory associated with curved trajectories. The newly proposed closure model is applied to large-eddy simulation (LES) of idealized tornadoes. The results show that the normal surface-shear-stress component is a source of additional dynamic instability, which provides an extra pathway for the development of turbulent motions. Unlike the eddy-viscosity closure, the pseudo-second-order closure is capable of triggering turbulence in the absence of any random perturbation imposed via the initial and lateral boundary conditions. Tornadoes in the transient state may be especially sensitive to turbulence memory, which can enhance near-surface convergence and delay the formation of a central downdraft.