Role of Vortex Structures in the Surface Layer in the Radiation Interaction between Underlying Surface and Air
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of Vortex Structures in the Surface Layer in the Radiation Interaction between Underlying Surface and Air B. M. Koprov† and V. M. Koprova, * a
Obukhov Institute of Atmospheric Physics, Russian Academy of Sciences, Moscow, 119017 Russia *e-mail: [email protected] Received January 30, 2019; revised March 11, 2020; accepted April 1, 2020
Abstract—By the 1950s, it was revealed that assumptions of the semiempirical statistical theory of the surface layer created by A.S. Monin and A.M. Obukhov, strictly speaking, fail. The existence of organized (coherent) structures in the surface layer and their main role in the advective (turbulent) vertical transfer of heat, momentum, and impurities have been experimentally proved. The decisive role of the radiation in the formation of the air temperature profile is obvious. This work is an attempt to qualitatively describe how organized vortex structures interact with radiation thermal conductivity during heat transfer from the underlying surface to the atmosphere. Keywords: surface layer, radiation exchange, coherent structures, vortex structures, turbulent transfer DOI: 10.1134/S0001433820040052
INTRODUCTION The semiempirical statistical theory of the surface layer created by A.S. Monin and A.M. Obukhov [1] (hereinafter, the М ∗ О theory) played a great part in related investigations. Recent review [2] was dedicated to its 50th anniversary. The authors of the theory considered it possible to neglect the radiation heat flux when developing the theory. The stationarity and the absence (by default) of organized structures belong to main assumptions of the М ∗ О theory. Theoretical studies of the Earth’s atmosphere as a thin gas shell of a rotating ball affected by the solar radiation [3–5] began at the turn of the 20th century under the influence of astrophysical studies of the atmospheres of the Sun and other stars. They showed the vertical profile of the air temperature to be mainly determined by the IR radiation exchange between the surface and the atmosphere: the Earth’s surface, heated by direct solar radiation (which losslessly propagates through the Earth’s atmosphere), generates IR radiation, which is then absorbed by the atmosphere. Stationarity is usually understood as the time invariance of the mean air temperature and wind speed and the second moments of variations. The main parameters of the М ∗ О theory are the vertical turbulent heat flux c pρw ' T ' and vertical flux of momentum ρw' u', which are considered altitude independent; the buoyancy parameter g T ; and the alti† Deceased.
tude z. Here, cp is the specific heat at a constant pressure, ρ is the air density, u' and w ' are the variations in the horizontal and vertical wind speeds, T and T′ is the temperature and its variations, and g is the acceleration of gravity. The horizontal bar indicates time averaging. To describe the surface layer, a coordinate system is used where the x axis is directed along the middle wind and the z axis is vertically directed. The Earth rotation is not taken into account, i.e., the
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