Abstract
The first results of a laboratory simulation of the Kolmogorov flow on a spherical surface are described. The primary laminar regime was found to be a system of zonal laminar jets of alternating directions. When the first critical value is passed, the primary regime loses its stability, and on its background a secondary vortex quasi-periodic regime with low frequency is formed. With a further increase in the Reynolds number and when the second critical value is passed, this vortex regime becomes unstable and self-excited oscillations emerge in the flow. Specifically, it was found that, if the spherical layer radius is chosen as a length scale, the wavelengths of perturbations in the vortex regime fall in the range of maximum intensity in the spectrum of the horizontal component of wind speed at the tropopause level. We explain the maximum peak shift in the wind spectrum on synoptic time scales when the observational height increases from 3000 km in the surface layer up to 8000–10000 km in the upper troposphere and lower stratosphere.
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References
A. M. Obukhov, “The Kolmogorov Current and Its Laboratory Simulation,” Uspekhi Mat. Nauk 38(4), 101–111 (1983).
V. A. Dovzhenko, Yu. V. Novikov, and A. M. Obukhov, “Modeling the Process of Vortex Generation in an Axially Symmetrical Azimuthal Field by the Magnetohydrodinamical Method,” Izv. Akad. Nauk SSSR, Fiz. Atmos. Okeana 15(11), 1199–1202 (1979).
F. V. Dolzhanskii and G. S. Golitsyn, “Laboratory Simulation of Global Geophysical Currents,” Izv. AN SSSR. FAO 13(8), 795–818 (1977).
G. P. Williams, “Planetary Circulations: Barotropic Representation of Jovian and Terrestrial Turbulence,” J. Atmos. Sci. 35, 1399–1426 (1978).
A. M. Batchaev, “A Technique for Simulating Large-Scale Atmospheric Currents and an Instrument for Its Implementation,” RF Inventor’s Certificate no. 2388062, 2008 (unpublished).
Yu. N. Belyaev, A. A. Monakhov, and I. M. Yavorskaya, “Stability of the Spherical Couette Flow in Thick Layers at the Rotating Internal Sphere,” Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 2, 9–15 (1978).
D. S. Zimmerman, S. A. Triana, and D. P. Lathrop, “Bi-Stability in Turbulent, Rotating Spherical Couette Flow,” Phys. Fluids 23(6), 065104 (2011).
I. Van der Hoven, “Power Spectrum of Horizontal Wind Speed in the Frequency Range from 0.0007 to 900 Cycles Per Hour,” J. Meteorol. 14, 160–164 (1957).
F. Fielder and H. A. Panofsky, “Atmospheric Scales and Spectral Gaps,” Bull. Amer. Meteorol. Soc. 51(12), 1114–1120 (1970).
G. D. Nastrom and K. S. Gage, “A Climatology of Atmospheric Wavenumber Spectra of Wind and Temperature Observed by Commercial Aircraft,” J. Atmos. Sci. 42, 950–960 (1985).
A. M. Batchaev, “Experimental Study of Above-Critical Regimes of the Kolmogorov Flow on a Cylindrical Surface,” Izv. Akad. Nauk SSSR, Fiz. Atmos. Okeana 24(8), 844–851 (1988).
A. M. Batchaev, “Self-Oscillations in an Elementary Cell of a Doubly Periodic Quasi-Two-Dimensional Flow,” Izv., Atmos. Ocean. Phys. 39(4), 401–412 (2003).
A. M. Batchaev and V. A. Dovzhenko, “Laboratory Simulation of the Loss of Stability of Periodic Zonal Flows,” Dokl. Akad. Nauk SSSR 273(3), 582–584 (1983).
H.-P. Huang and A. Robinson, “Two-Dimensional Turbulence and Persistent Zonal Jets in a Global Barotropic Model,” J. Atmos. Sci. 55, 611–632 (1998).
A. M. Batchaev and M. V. Kurganskii, “On the Instability of the Periodic Flow of a Weakly Stratified Fluid,” Izv. Akad. Nauk SSSR, Fiz. Atmos. Okeana 22(1), 3–9 (1986).
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Original Russian Text © A.M. Batchaev, 2012, published in Izvestiya AN. Fizika Atmosfery i Okeana, 2012, Vol. 48, No. 6, pp. 733–738.
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Batchaev, A.M. Laboratory simulation of the Kolmogorov flow on a spherical surface. Izv. Atmos. Ocean. Phys. 48, 657–662 (2012). https://doi.org/10.1134/S0001433812060035
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DOI: https://doi.org/10.1134/S0001433812060035