A. S. Monin

The Structure of Atmospheric Turbulence

Theoretical and experimental data are given for the statistical characteristics of random fields of wind velocity and turbulent fluctuations of temperature in the lowest layer of the atmosphere. Fluctuations are considered at one and two space time points. Probability distributions, moments, autocorrelation and structure functions, spectra and cross-spectra are studied. Some dimensionless characteristics (universal functions) are determined by means of Kolmogorov’s similarity theory for small eddies and similarity theory for fully developed turbulence proposed by Oboukhov and Monin. In addition a short summary is given of works on pressure fluctuations, turbulent accelerations, turbulent diffusion and also on the problem “fluctuations and waves”.

One-Dimensional Models

The vertical structure of the atmosphere is known to vary quite appreciably from place to place, especially from latitude to latitude, and also in time, especially from season to season. In spite of this, however, the mean vertical structure is such an expressive climatic characteristic of the state of the atmosphere as a whole that meteorologists have coined the special term “standard atmosphere” and have worked out for it a whole series of increasingly accurate empirical models.

The General Circulation of the Atmosphere

Large-scale processes in the atmosphere (synoptic and global processes) require an individual description. Since the large-scale movements are practically quasi-static and nondiverging, they can be described in an appropriate form by simplified equations of hydrodynamics (in which for the quasi-static approximation it is necessary to use the so-called “traditional approximation” for the Coriolis acceleration; in addition, since the heights z = r − a are small in comparison with the distance r from the Earth’s center, it is advisable everywhere to use the Earth’s radius a instead of r). The equation of hydrostatics is

Three-Dimensional Models

\partial .p/\partial z = - g\varrho

The Atmospheric Boundary Layer

where g is the free-fall acceleration, and z is the height above the surface of the geoid (often referred to as “sea level”). Using the complement of the latitude θ = π − ϕ and the longitude λ, and designating the velocity components as v z , vθ, and vλ, we can write the continuity equation (the condition of nondivergence of the velocity field) as follows:

Statistical Fluid Mechanics, Vol. II

{{\partial {\upsilon _z}} \over {\partial z}} + {1 \over {a\,\sin \,\theta }}\left( {{{\partial {\upsilon _\theta }\,\sin \,\theta } \over {\partial \theta }} + {{\partial {\upsilon _\lambda }} \over {\partial \lambda }}} \right) + 0