Irkutsk, Russian Federation
Irkutsk, Russian Federation
Irkutsk, Russian Federation
We present the results of numerical simulations of normal modes of the mean flow due to the superposition of cyclonic and anticyclonic vortices at high latitudes. Such a flow structure is often observed in the upper troposphere — the lower stratosphere in winter. Our aim is to identify normal modes in the oscillation spectrum that resemble torsional oscillations. We solve the problem numerically, using a barotropic quasi-geostrophic model. Additionally, we estimate the dependence of the normal modes on experimental parameters (the number of spherical harmonics in the stream function field expansion, the parameterization of viscosity and hyperviscosity). The simulation results show that flow instability almost always increases with increasing amplitude of the anticyclonic vortex to varying degrees at different viscosities and different numbers of harmonics in the field expansion. The spatial structure of the most unstable normal modes changes most chaotically when the experiment parameters and the mean flow change. This significantly complicates the interpretation of real oscillations in terms of normal modes, including the interpretation of torsional oscillations. Axisymmetric normal modes are often present in the spectrum, but they do not have all the properties of torsional oscillations and do not dominate the spectrum.
hydrodynamics, atmosphere, normal modes, torsional oscillations
1. Blackmon M.L., Lee Y., Wallace J.M. Horizontal structure of 500 mb height fluctuations with long, intermediate and short time scales. J. Atmos. Sci. 1984a, vol. 41, pp. 961–980. DOI:https://doi.org/10.1175/1520-0469(1984)041<0961:HSOMHF>2.0.CO;2.
2. Blackmon M.L., Lee Y., Wallace J.M., Hsu H. Time variation of 500 mb height fluctuations with long, intermediate and short time scales as deduced from lag-correlation statistics. J. Atmos. Sci. 1984b, vol. 41, iss. 6, pp. 981–991. DOI: 10.1175/ 1520-0469(1984)041<0981:TVOMHF>2.0.CO;2.
3. Branstator G. A striking example of the atmosphere’s leading travelling pattern. J. Atmos. Sci. 1987, vol. 44, pp. 2310–2323.
4. Branstator G., Held I. Westward propagating normal modes in the presence of stationary background waves. J. Atmos. Sci. 1995, vol. 52, pp. 247–262.
5. Danilov S.D., Gurarie D. Quasi-two-dimensional turbulence. Physics – Uspekhi. 2000, vol. 170, no. 9, pp. 863–900. DOI:https://doi.org/10.1070/PU2000v043n09ABEH000782.
6. Dikii L.A. Theory of Vibrations of the Earth's Atmosphere. Leningrad, Gidrometeoizdat Publ., 1969, 194 p. (In Russian).
7. Dymnikov V.P., Skiba Yu.N. Barotropic instability of zonally symmetric atmospheric flows. Calculation Processes and Systems. Moscow, Nauka Publ., 1986, iss. 4, pp. 63–104. (In Russian).
8. Dymnikov V.P., Filatov A.N. Stability of Large-Scale Atmospheric Processes. Moscow, 1988, 140 p. (In Russian).
9. Dymnikov V.P. Stability and Predictability of Large-Scale Atmospheric Processes. Moscow, IVM RAN Publ., 2007. 283 p. (In Russian).
10. Dikpati M., Gilman P.A. Analysis of hydrodynamic stability of solar tachocline latitudinal differential rotation using a shallowwater model. Astrophys. J. Papers. 2001, vol. 551, no. 1, pp. 536–564. DOI:https://doi.org/10.1086/320080.
11. Kasahara A. Effect of zonal flows on the free oscillations of a barotropic atmosphere. J. Atmos. Sci. 1980, vol. 37, iss. 5, pp. 917–929. DOI:https://doi.org/10.1175/1520-0469(1980)037<0917: EOZFOT>2.0.CO;2.
12. Koval A.V., Gavrilov N.M,. Pogoreltsev A.I, Shevchuk N.O. Influence of solar activity on penetration of traveling planetary-scale waves from the troposphere into the thermosphere. J. Geophys. Res.: Space Phys. 2018, vol. 123, no. 8. P. 6888–6903. DOI:https://doi.org/10.1029/2018JA025680,08.2018.
13. Large-Scale Dynamic Processes in the Atmosphere. Moscow, Mir Publ., 1988, 430 p. (In Russian).
14. Longuet-Higgins M.S. Planetary waves on a rotating sphere. Proc. Royal Soc., Series A. 1964, vol. 279, iss. 1379, pp. 446–473.
15. Longuet-Higgins M.S. The eigenfunctions of Laplace’s tidal equation over a sphere. Math. and Phys. Sci. London, 1968, vol. 262, pp. 511–607. DOI:https://doi.org/10.1098/RSTA.1968.0003.
16. Madden R.A. Large-scale free Rossby waves in the atmosphere – an update. Tellus A: Dynamic Meteorology and Oceanography. 2007, vol. 59, pp. 571–590. DOI:https://doi.org/10.1111/j.1600-0870.2007.00257.x.
17. Mordvinov V.I., Latysheva I.V. Theory of General Atmospheric Circulation, Variability of Large-Scale Processes. Irkutsk, ISU Publ., 2013, 197 p. (In Russian).
18. Mordvinov V.I., Zorkaltseva O.S. Normal mode as a cause of large-scale variations in the troposphere and stratosphere. Izvestiya, Atmos. and Ocean. Phys. 2022, vol. 58, no. 2, pp. 140–149. DOI:https://doi.org/10.1134/S0001433822020098.
19. Mordvinov V., Devyatova E., Tomozov V. Hydrodynamic instabilities in the tachocline due to layer thickness variations and mean flow inhomogeneities. Solnechno-zemnaya fisika [Solar-Terr. Phys.]. 2013, iss. 23, pp. 3–12. (In Russian).
20. Mordvinov V.I., Devyatova E.V., Tomozov V.M. Influence of the magnetic field and the mean flow configuration on spatial structure and growth rate of normal modes. Solar-Terr. Phys. 2023, vol. 9, iss. 4, pp. 123–135. DOI:https://doi.org/10.12737/stp-94202315.
21. Pogoreltsev A.I., Kanukhina A.Yu., Suvorova E.V., Savenkova E. Variability of planetary waves as a signature of possible climatic changes. J. Atmos. Solar-Terr. Phys. 2009, vol. 71, iss. 14-15, pp. 1529–1539. DOI:https://doi.org/10.1016/J.JASTP.2009.05.01
22. Simmons A.J., Wallace J.M., Branstator G.W. Barotropic wave propagation and instability, and atmospheric teleconnection patterns. J. Atmos. Sci. 1983, vol. 40, no. 6, pp. 1363–1392.
23. Yaglom M.A. Dynamics of large-scale processes in the barotropic atmosphere. Izvestiya AN SSSR. Seriya geofizicheskaya [Proc. Academy of Science of USSR. Ser. Geophys.]. 1953, no. 4, pp. 346–369. (In Russian).
24. Zorkaltseva O.S., Mordvinov V.I., Devyatova E.V., Dombrovskaya N.S. Method for calculating torsional oscillations in Earth's atmosphere from NCEP/NCAR, MERRA-2, ECMWF ERA-40, and ERA-INTERIM. Solar-Terr. Phys. 2019, vol. 5, iss. 1, pp. 69–76. DOI:https://doi.org/10.12737/stp-501201910.