Turbulence in the Atmosphere and Hydrosphere

In most cases, the motion of air in the atmosphere and of water in the hydrosphere is of a turbulent nature. Turbulence in the atmosphere and hydrosphere is important because it gives rise to the following: the exchange of momentum and heat between the atmosphere and the ocean (including the generation of wind currents and ocean waves); evaporation from the surface of the ocean and the land; the vertical transport of heat, moisture, salts, dissolved gases, and various pollutants; the dissipation of kinetic energy; and the scattering and amplitude and phase fluctuations of acoustic, light, and radio waves, as seen, for example, in the twinkling of stars, fluctuations of radio signals from spacecraft, and the propagation of television signals over very long distances. The specific features of turbulence in the atmosphere and hydrosphere are a very broad spectrum of turbulence scales (from millimeters to thousands of kilometers) and the considerable influence of the vertical density distribution of the medium on the development of small-scale turbulence.

The spectrum of turbulence scales in the atmosphere is divided into a synoptic region (macroturbulence), which has a scale much greater than the scale height of the atmosphere H ~ 10 km and is characterized by quasi-two-dimensional (quasi-horizontal) turbulent inhomogeneities, and a micrometeorological region, which has a scale much smaller than H and is characterized by essentially three-dimensional inhomogeneities. In the intermediate meso meteorological region, any kind of strong turbulence is rare. Macroturbulence derives energy from large-scale inhomogeneities of the heat flux to the atmosphere from the underlying surface and expends energy primarily on the generation of microturbulence when the vertical wind-velocity gradients are hydrody-namically unstable.

Unstable stratification is the source for microturbulence, and stable stratification provides the sink for the energy of microturbulence. Microturbulence is strong in the case of unstable stratification and weak in the stable case. The properties of microturbulence are simplest in the lowest atmospheric layer, which is a few tens of meters thick and in which the vertical turbulent momentum flux T and the vertical turbulent heat flux q are constant. Under quasi-steady-state conditions with horizontal homogeneity, the characteristics of the large-scale components of such turbulence are determined by the buoyancy parameter β = g/T₀ and the quantity q/c_pρ (where g is the acceleration of gravity, c_p is the specific heat of the air, ρ is the density of the air, and T₀ is the mean temperature), in addition to height z and the friction velocity v* = (τ/ρ)^½. Measured on scales of length , time L/v*, and temperature q/c_ppv*, these characteristics are universal functions of the dimensionless height z/L or of the Richardson number, which is determined by the height,

where v is the wind velocity and T is the temperature.

The properties of oceanic microturbulence are determined by the presence of a vertical microstructure in the ocean, that is, long-lived quasi-homogeneous layers that are not more than ~1 m thick and separated by discontinuity surfaces of temperature and salinity. The presence of such layers is typical of a very stably stratified liquid. The turbulence concentrated in these layers is weak; that is, it cannot disrupt the discontinuity surfaces that separate the layers. In addition, it has small Reynolds numbers, which are determined by the thicknesses of the layer. This turbulence, therefore, is not in universal statistical equilibrium and is determined by the characteristics, rather than the depth, of each specific layer.