Abstract
Turbulent flows of a viscous incompressible fluid in a layer between rotating concentric spheres under the action of the modulation of the velocity of one of the spheres have been studied experimentally and numerically. The form of spectra of turbulent pulsations of the azimuthal velocity depends on the sphere whose rotational velocity is modulated, as well as on the amplitude and frequency of modulation. The possibility of the formation of turbulence with spectra qualitatively similar to spectra obtained in measurements in the upper atmosphere is established: with the slope close to –3 at low frequencies and close to –5/3 at high frequencies and with the negative longitudinal velocity structure function of the third order. It has been shown that such spectra are formed in the regions of a flow that are strongly synchronized under the action of the modulation of the rotational velocity.
Highlights
Two inertial intervals are usually identified corresponding to energy transfer at low wave numbers and enstrophy transfer at high wave numbers [3]
The direction of the cascade is determined by the sign of the third order longitudinal velocity structure function [5], which is defined as DLLL = 〈[u(l) – u(l')]-3 〉, where u is the velocity at the spatially separated points l and l' and angular brackets mean averaging over the ensemble of realizations
With a further increase in the modulation amplitude, the spectra can be transformed to the form characteristic of two-dimensional turbulence
Summary
Despite the existing explanations [1, 8, 9]reasons for the inverse position of spectral regions, as well as the possibility of reproducing this phenomenon under laboratory conditions, are as yet unclear Both viscous dissipation [10]and vertical motions that are components of large scale circulation [6] prevent two-dimensional turbulent flows in the atmosphere. Large scale circulation exists in turbulent flows induced by the rotation of the boundaries of the spherical layer, which is responsible for the motion of viscous incompressible fluid sandwiched between them [11] It is exactly why the model spherical Couette flow is studied in this work for the qualitative simulation of processes in the atmosphere.
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