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Cognitive chaos: turbulence in Earth system

Scientific organization
in Russia: University of Nizhny Novgorod
Academic degree
Chief Scientist / RSF grant holder
Scientific discipline
Earth Sciences, Ecology & Environmental Management
Cognitive chaos: turbulence in Earth system
Turbulence plays vitally important role in nature. In particular, it links geospheres via strongly turbulent boundary layers and performs vertical transport of energy, matter and momentum across atmosphere and hydrosphere. It never collapses even in very stable stratification and never dominates even in extremely strong convection. This happens due to tricky self-control mechanisms keeping chaos and order in the atmosphere and hydrosphere in the shares optimal for the Earth system.
Atmosphere Boundary layers, Chaos, Convection, Earth system, Hydrosphere, Order, Turbulence, Stratification, Self-control, Vertical transport
  • It is widely recognised that in very stable stratifications, at Richardson numbers (Ri) exceeding the critical value, Ric ~ 0.25, turbulence inevitably decays and the flow becomes laminar. This is so, indeed, in the low-Reynolds-number (Re) flows, e.g., in some lab experiments; but this is not a hard-and-fast rule. The atmosphere and hydrosphere are almost always turbulent in spite of the strongly supercritical stratification with typical values of Ri varying in the interval 10 < Ri < 102. Until recently, this paradox has remained unexplained.
  • The key mechanisms of the seemingly paradoxical self-preservation of the very-high-Re geophysical turbulence are (i) conversion of the turbulent kinetic energy unto potential energy and (ii) self-control of the negative (down-gradient) turbulent heat flux through efficient generation of the positive (counter-gradient) heat transfer by the turbulent potential energy (Zilitinkevich et al., 2007, 2008, 2009, 2013). It is precisely due to this loop that turbulence is maintained in supercritical stratifications. Moreover, at Ri > Ric the familiar “strong-mixing turbulence” regime, typical of boundary-layer flows and characterised by the practically invariable turbulent Prandtl number  ~ 1 (the so-called “Reynolds analogy”), gives way to the newly discovered “wave-like turbulence” regime (wherein  sharply increases with increasing Ri), rather than to the laminar regime as is often the case in the small-scale lab experiments.
  • It is precisely the wave-like turbulence that dominates the bulk of the atmosphere and ocean beyond boundary layer and convective zones. Modellers have long been aware that turbulent heat transfer in the free atmosphere/ocean is much weaker than the momentum transfer. The new theory has given authentic formulation for this heuristic rule and provided physically grounded method for modelling geophysical turbulence up to very stable stratifications.
  • Turbulence is ever present in the atmosphere and ocean and performs the following vitally important “services”: (i) transports energy, matter and momentum in the vertical across the fluid geospheres, and (ii) links geospheres via strongly turbulent planetary boundary layers (PBLs) into interconnected climate- and other Earth systems.
  • Turbulent mixing is strong in PBLs and very weak beyond PBLs – in the free atmosphere and free ocean. PBLs couple the atmosphere, hydrosphere, lithosphere and cryosphere into a hierarchy of interconnected systems, including the global climate system. PBLs host 90% of the biosphere and the entire anthroposphere (our habitat).
  • Convective motions driven by the potential energy of unstable stratification develop over warm Earth surface (or in clouds), and very efficiently transfer heat from the surface upward – thus preventing extremes and moderating thermal conditions at the Earth’s surface. Conventional theory, which treated convective mixing as usual turbulence, has got in conflict with modern experimental evidence. Observations of turbulent convection in nature, as well as large-eddy simulation (LES) and direct numerical simulation (DNS) of turbulent convection have revealed, besides really chaotic motions, large-scale self-organised rolls or cells similar to secondary circulations in lab experiments, traditionally considered as artificial, parasitic phenomena. Self-organised convective cells in viscous convection are known since Benard (1900) and Rayleigh (1916), but self-organised rolls have no analogy in viscous convection. They are driven by large-scale turbulent instability caused by the non-gradient horizontal heart flux (Elperin et al, 2002, 2005). Self-organised convective motions are missed in universally recognised theories, such as the heat/mass transfer law: Nu = 0.14 Ra1/3, the Monin-Obukhov similarity theory, etc.
  • The shear-free turbulent convection exhibits the following crucially important mechanism disregarded in the conventional theory. Large-scale self-organised convective cell includes the near-surface convective winds towards the plume base. The latter generate mechanical turbulence which, in turn, enhances the heat and mass transfer up to two orders of magnitude.