Special ClimaTea

Speaker:Professor Sergej Zilitinkevitch  from Finnish Meteorological Institute (FMI) University of Helsinki

Title: "Non-gradient turbulent fluxes and inverse cascades in stratified turbulence: towards revision of conventional paradigm"

Abstract: Current vision and modelling of stratified geophysical turbulence are to a large extent based on conventional paradigm leaving no alternative to the downgradient turbulent transports (quantified via turbulent viscosity, heat conductivity and diffusivity) and the forward cascades of kinetic energy and other properties of turbulence – towards molecular dissipations. These concepts underlie turbulence-closure models, theory/modelling of turbulent diffusion, and Monin-Obukhov Similarity Theory (MOST) of the surface-layer turbulence.

In this framework, turbulence in super-critically stable stratifications typical of free atmosphere and ocean thermocline is considered as principally the same as in sub-critically stable boundary layers, but just weak due to strong static stability and weak velocity shears. In unstable stratification, convective turbulence generated by buoyancy forces is considered as principally the same as mechanical turbulence generated by mean velocity shears and, thus, subjected to the forward cascades.  

Recent observational evidences have disclosed principal drawbacks of conventional theory of stratified turbulence and intolerable uncertainties in its modelling. Nevertheless, neither MOST nor traditional turbulence-closure nor turbulent diffusion models are seriously questioned. Their drawbacks root in the commonly recognised paradigm attributed to Kolmogorov (1941a,b; 1942). However, Kolmogorov considered the shear-generated turbulence in neutrally stratified flows where his major concepts:

• only forward energy cascade – from larger to smaller eddies, towards dissipation
• and only down-gradient turbulent fluxes, serve as reasonable approximations. Moreover, Kolmogorov was not responsible for the extension of his paradigm to stratified turbulence. This was made by his followers without proof.

This talk demonstrates that conventional paradigm makes a Procrustean bed for the theory of turbulence in both unstable stratification (Zilitinkevich, 1973, 2013; Zilitinkevich at al., 2006) and strongly stable stratification (Zilitinkevich et al., 2008, 2013). We highlight its restrictive nature; demonstrates miscarriages of conventional theory as applied to essentially stratified flows; and outline Energy- and Flux-Budget (EFB) turbulence-energetics and closure theory accounting for non-gradient turbulent fluxes in both stable and unstable stratifications, inverse energy cascade in convective turbulence, and PBL-scale self-organised convective motions generated via inverse cascades.