Modelling Turbulence Effect in Formation of Zonal Winds

Abstract

A turbulence-affected mechanism of formation of zonal winds in the Earth's troposphere is discussed from the perspective of the theory of rotationally anisotropic turbulence (the RAT theory). The turbulence effect is explained as an action of the turbulence rotational viscosity introduced within the RAT theory to characterize the shear in relative rotation (determined as the difference between the average angular velocity of eddy rotation and the vorticity of the average velocity field). The effect manifests in the form of an additive correction to the wind velocity predicted by the geostrophic approach. It is shown that the accounted turbulence effect decreases the westerlies' velocity predicted by the geostrophic approach at lower latitudes and can be used to explain the formation of easterlies (trade winds) in the equatorial zone without any necessity of assigning the geopotential a local minimum, at the Equator which is required to explain the trade winds within the purely geostrophic approach.

The structure of average turbulent flow field

“…(12)- (14) are, respectively, the averaged NavierStokes equation, the average equation following from the Navier-Stokes equation by its vector multiplication from the right by R, and the difference of the equations for turbulence energy K and energy K Ω with the latter following from (13) after its scalar multiplication by Ω. The deduction procedure specifies the terms in (13) and (14) as follows:…”

“…The removal becomes possible due to the definition of characteristics of the rotational degrees of freedom of the fluctuating constituent of the velocityfield, interpreted as the measure of the average effect of eddy rotation, and the medium's turbulence split into orientated and non-orientated constituents, respectively interpreted as the large-scale and the small-scale turbulence constituents, along with the specification of the CTM as describing the non-orientated turbulence constituent. The applications of the RAT theory for describing flows in channels, round tubes and between rotating cylinders (including pulsating flows in round tubes) [7], for description of MHD turbulent flows in plain channels for different mutual orientations of the magnetic field and the motion characteristics [8] and for discussion of several problems in geophysics (the reaction of the ocean upper layer to periodic heating and cooling [9,10], the diffusion effect in the formation of the Gibraltar Salinity anomaly [11], the turbulence effects' contribution to the net transport of the Antarctic Circumpolar Current [12] and to the formation of zonal winds [13], the effects of eddy-to-mean energy transfer in geophysical turbulent jets (on the Gulf Stream example) [14] and in the formation of eddy-driven flows over varying bottom topography in natural water bodies [15]) have recommended this theory as notably expanding the competence of turbulence mechanics in discussing various turbulence-related problems, the solution of which is considered sufficient in average terms.…”

A modification of the classical Ekman model accounting for the Stokes drift and stratification effects

“…2). The applications of the RAT theory [10][11][12][13][14][15][16][17][18][19][20][21][22]35,36] have so far proven this theory to be a tool complementing the variety of tools for discussing oceanographic and other related problems. Concerning the Ekman layer it is shown that the application of the RAT theory embraces the Stokes drift and stratification effects in one single model.…”