Turbulence in Atmospheric Surface Layer Revisited (Invited Presentation)

Monin-Obukhov (1954) Similarity Theory (MOST) of the surface-layer turbulence was derived via dimensional analysis from similarity and scaling reasoning in frames of conventional turbulence paradigm attributed to Kolmogorov (1941). We recall that Kolmogorov considered the shear-generated turbulence in neutrally stratified flows, whereas subsequent extension of his vision to any stratification was done by his followers without proof. Anyhow, MOST was the first theory answered the challenging question of the effects of stratification on turbulence and remained the most quoted paper in atmospheric sciences over many decades. In the course of time, more and more evidence of its poor applicability to unstable and strongly stable stratifications was collected and now approached critical level. The talk focused on the major failures of MOST listed below.

In unstable stratification, MOST does not distinguish between

• Shear-generated turbulence consisted of dynamically unstable eddies that break down to perform direct cascade of kinetic energy from larger to smaller scales, towards dissipation
• Buoyancy-generated turbulence consisted of uprising plumes that merge to perform inverse cascade – from smaller to larger scales towards self-organised “convective winds”

The point is that conventional paradigm and, hence, MOST do not envisage inverse cascades, thus offering erroneous picture of turbulence in unstable stratification, particularly, of anisotropy, horizontal fluxes and 3-dimensional diffusivity (Zilitinkevich 1973, 2010, 2013). Furthermore, MOST ignores self-organised convective winds and extra turbulence generated by convective-wind shears close to the surface. This causes underestimation of the near-surface heat and matter transfer in calm-weather convection by an order of magnitude (Zilitinkevich et al., 2006).

In moderately stable stratification, MOST serves as a good approximation; but in very stable stratification it wrongly predicts principally similar formulation of eddy viscosity and heat conductivity. The latter implies unrealistic degeneration of atmospheric turbulence in the conditions where it factually ever exists, e.g., in the surface layer over rough surfaces and in the free atmosphere (Zilitinkevich et al, 2007a, 2008a, 2009, 2013). In modelling practice, this unacceptable fault is corrected without physical explanation.

Moreover, MOST disregards interaction between the surface layer and the rest of PBL, which makes it fully erroneous as applied to long-lived PBLs crucially dependent on the basic-state stratification in free atmosphere (Zilitinkevich and Esau, 2002, 2007).

In spite of well-documented inconsistencies, MOST has not been principally revised. We derive alternative theory from basic physical principals (rather than dimensional analysis) in frames of revised paradigm accounting for real features of stratified turbulence (Zilitinkevich, 2010):

• Non-gradient turbulent transports along with down-gradient transports
• Inverse energy cascades, particularly in convective turbulence, along with direct cascades in shear-generated mechanical turbulence eddies
• Self-organised motions, such as cells of rolls in convective layers, complementing usual mean flow and strongly enhancing drag and heat/mass transfer at the surface

We present illustrative examples were MOST fails and alternative theory explains why it fails.