The index cycle ( vascillation ) is a phenomenon of hydrodynamic instability of rotation of an unevenly heated liquid or gas, originally detected as a quasiperiodic change in the index of zonal atmospheric circulation [1] [2] . A characteristic feature of this instability is the periodic exchange of energy between the ordered and disordered motion. A similar process is observed in ocean currents, in laboratory experiments with a rotating unevenly heated liquid, in the atmospheres of other planets, possibly in the liquid core of the planet, in rotating stars and in accretion disks .
Content
Atmospheric circulation indices
- Karl-Gustav Arvid Rossby proposed characterizing the rotation of the atmosphere relative to the Earth as a “circulation index” (Rossby) —the average zonal geostrophic wind speed calculated for each zone by the average meridional gradient of atmospheric pressure (or the height of the isobaric surface). K. - G. Rossby recommended dividing the troposphere into the following latitudinal zones, each of which is characterized by its own circulation index.
| Winter | Summer | Wind |
| 20 o −25 o | 20 o −40 o | Oriental |
| 35 about −55 about | 40 o −65 o | west |
| 55 o −70 o | > 65 about | Oriental |
- Ekaterina Nikitichna Blinova [3] suggested evaluating the relative rotation of the atmosphere by the index where - the average in the latitudinal zone of 45 about −65 about the angular velocity of rotation of the troposphere relative to the Earth, - the angular velocity of the Earth. (The value of the Blinova index A = 1 corresponds to a linear wind speed of ~ 23 cm / s.)
- P. Webster and J. Keller [4] used the ratio of the kinetic energy of turbulence to the kinetic energy of ordered movement, measured in three, to analyze the general atmospheric circulation by observing the movement of balanced balloons in the international experiment “EOL” (1972). latitudinal zones: 30 о −40 о , 40 о −50 о , 50 о −60 о of the Southern Hemisphere.
- The degree of ordering of atmospheric circulation can be measured by informational entropy . Using the informational entropy of the height of the isobaric surface in the hemisphere [5] turned out to be a very convenient method for studying the phenomenon of the index cycle.
Other methods for quantifying the type of general atmospheric circulation are also known.
Index loop phenomenon
- As early as 1878, I. B. Spindler noted that cyclones come from the Atlantic to the European continent, not alone, but in series. This fact indirectly indicates that in the atmosphere there may exist some kind of global periodic process that affects cyclogenesis.
- In 1915, B. P. Multanovsky [6] noted that synoptic processes lend themselves to typing. He introduced the concept of "elementary synoptic process" into meteorology, the duration of which is about 2-4 days. According to B.P. Multanovsky, elementary synoptic processes are grouped in the "natural synoptic period" - a concept generated by the cyclical nature of synoptic processes.
- In 1944, H. Willett [7] [8] and K. —G. Rossby [9] (University of Chicago) found that a quasiperiodic alternation of different types of atmospheric circulation is observed in the atmosphere. A state with an increased rate of ordered circulation (“high index”), in which the energy of turbulent structures is lowered, alternate with the opposite situation (“low index”), in which the energy of turbulence (cyclogenesis) reaches a maximum. The discovered meteorological phenomenon has received the name "index cycle" .
In the atmosphere
According to H. Willett and K. —G. The Rossby index cycle period is approximately 3-4 weeks. To accurately determine the period of the index cycle, the spectrum of series of observations both for the circulation indices and other characteristics of the state of the atmosphere was repeatedly studied. However, the spectrum of atmospheric processes turned out to be rather complicated, containing many harmonics in the interval of 5-50 days. It is not clear which harmonic is responsible for the main process, and which are secondary. The temporal spectrum of fluctuations in the meteorological characteristics of the atmosphere contains distinct daily and annual cycles and their harmonics. The existence of other hidden periodic processes raises great doubts because of their low statistical significance [10] . The determination of the index cycle period from the spectrum of time series is complicated due to the fact that the amplitude and the cycle period change in the atmosphere not only during the year, but also from fluctuation to fluctuation, which generated a general skepticism about the existence of this phenomenon in nature.
The study of the energy characteristics of the atmosphere, especially the ratio of the energy of turbulence to the energy of ordered motion, turned out to be more informative in comparison with the Rossby index or the Blinova index. An analysis of the index cycle period in the EOL experiment in the southern hemisphere yielded a value of 18-23 days. A study of the duration of the index cycle in the northern hemisphere from the spectra of kinetic and available potential energy [11] led to a value of the index cycle period of 20–26 days.
It is of interest to study the spectrum of oscillations of information entropy of the characteristics of the general circulation of the atmosphere. A study of the informational entropy of the height of the isobaric surface of 500 hPa at a latitude of 50 ° for the winter half of the year in the Northern Hemisphere showed [5] that this quantity, which characterizes the measure of atmospheric ordering and is responsible only for the phenomenon of the index cycle, has one distinct spectral maximum corresponding to a period of 23 —24 days.
The period and amplitude of the index cycle depend on the temperature difference between the equator and the pole. The studied process proceeds in each hemisphere separately. The average annual value of the index cycle period in the northern hemisphere is about 25 days, and in the southern hemisphere - 20 days. In winter, the amplitude of the process increases; in summer, it decreases. In the northern hemisphere, the minimum value of the index cycle period is 22 days and falls in January. In summer, the period of oscillations increases rapidly, reaching a maximum of 53 days in July [12] .
The index cycle is also found in fluctuations in the inter-latitudinal difference in atmospheric pressure, known as Arctic oscillations . Familiar to sailors, the periodic increase in winds over the oceans, manifested in the “storm cycle”, especially expressed in the Southern Ocean [13] - this is the index cycle.
In the ocean
The qualitative similarity between the instability of jet flows in the atmosphere and in the ocean has been paid attention more than once. The development of meanders in the ocean current resembles the phenomenon of an index cycle. Similar to how the index cycle develops in the atmosphere, periodic passage of vortex packets with a period of ~ 1.5 years is observed in the North Atlantic [14] . This instability leads to fluctuations in temperature anomalies and ice cover. In numerical experiments on the mesoscale dynamics of the ocean based on the vortex-resolving quasi-geostrophic model [15] , self-oscillations were found that are qualitatively similar to the index cycle. A similar result was obtained in [16] . It has been found that in the ocean there are natural vibrations with a period of the order of 2 years, in which a periodic energy exchange occurs between turbulent and ordered motion.
The Gulf Stream is known to lose stability north of Cape Hatteras [17] . The theory of the phenomenon of the index cycle indicates that the hydrological conditions of this region of the ocean correspond to an oscillation period of ~ 1.8 years [18] . A similar estimate for the Antarctic circumpolar current gives a period of oscillations of this type of the order of 3 years.
The period and amplitude of oscillations of this type is determined by the density gradient of water in the direction perpendicular to the current velocity vector in the region in which it loses stability. On the other hand, the density gradient itself depends on the phase of the process. This situation entails the variability of the period of oscillations (quasiperiodicity). The instability of ocean currents leads to the fact that, associated with these currents, the heat transfer from the equator to the poles becomes variable, which affects the hydrological conditions and, accordingly, the weather, especially at high latitudes.
In the atmospheres of other planets
In the atmosphere of Jupiter , global oscillations resembling the index cycle are observed, with a period of the order of 11–13 years (the period of Jupiter's revolution around the Sun is ~ 12 years). Numerical experiments on modeling the dynamics of the atmosphere of Mars give reason to believe that oscillations with a period of 4-6 days during solstices are nothing more than an index cycle. In the atmosphere of Neptune , fluctuations were detected with a period of 21 years of unclear nature. A comparative analysis of fluctuations of the index cycle type in planetary atmospheres suggests that these processes are quantitatively and qualitatively similar to each other and, possibly, similar to the 11-year cycle of solar activity [19] .
Wascillation
In 1951, , working at the University of Cambridge on the problem of the origin of the geomagnetic field, set up experiments on convection in an unevenly heated rotating fluid. In his experiments, the tinted liquid was placed in the gap between two coaxial cylinders fastened together, the axis of which is located vertically and coincides with the axis of rotation. A constant temperature difference was maintained between the walls of the vessels. With some combinations of the angular velocity of rotation and the temperature difference between the cylinders, R. Hyde discovered an unusual phenomenon, which he called “vacillation” . - “wastillation, swing” [20] [21] . Wave-like structures appeared in the liquid, and the visible parameters — the length, amplitude, shape (slope) of these waves changed periodically. Secondary vortices appeared on the bends of the waves. The occurrence, development, and subsequent dissipation of wave and turbulent motions in R. Hyde's experiments was a new, previously unknown, self-oscillating hydrodynamic process in which the kinetic energy of a fluid was periodically pumped between turbulent and ordered components. Harold Jeffries drew R. Hyde's attention to the fact that the discovered by him oscillation is very similar to a similar phenomenon observed in the atmosphere - the index cycle.
In numerical experiments
To identify the physical nature of the oscillation phenomenon, Edward Lorenz applied a two-level spectral mathematical model of rotation of an unevenly heated liquid, reduced to a system of fourteen ordinary differential equations. Numerical experiments with this model showed that, depending on the speed of rotation and on the temperature difference between the center and the periphery of the cylindrical vessel into which the liquid is placed, four main types of flow are observed [22] :
- R1 - steady axisymmetric flow (named after "Hadley Mode"),
- R2 - stable wave mode of the flow (called "Rossby Mode"),
- R3 - wastillation,
- R4 - irregular (aperiodic) ("Rossby wave mode").
A numerical experiment confirmed that a phenomenon similar to the index cycle in the atmosphere is observed at the stability boundary. Along the way, E. Lorenz discovered that his numerical model is unstable with respect to small changes in parameters and initial conditions (“ Butterfly Effect ”). Studying the computational process in phase diagrams, he found that the solution of the system of equations modeling the oscillation has a special character, called the “strange Lorentz attractor” . This discovery gave rise, on the one hand, to a new look at the mechanism of turbulence, and, on the other hand, there was a reasonable doubt that it was possible in principle to numerically predict the development of synoptic processes in the atmosphere for periods comparable to the period of the index cycle. From which it follows that understanding the mechanism of the index cycle plays a key role in the development of numerical methods for weather forecasting .
Literature
- ↑ Index Cycle - Meteorological Dictionary
- ↑ Haltiner J. Martin F. Dynamic and physical meteorology. M .: Foreign literature. - 1960. - 436 p.
- ↑ E. Blinova, General atmospheric circulation and hydrodynamic long-term weather forecast, Tr. GMC, 1967. — Vol. 15. — C.3—26.
- ↑ Webster PJ, Keller JL Atmospheric variations: vacillation and index cycles // J. Atmos. Sci., 1975. — 32. — p. 1283–1300.
- ↑ 1 2 Kriegel A. M., Odintsov V. A., Sigarev S. M. On determining the period of the index cycle in the atmosphere // Bulletin of the Leningrad State. University. Ser. 7. — 1991. — Issue 4 (No. 28). — P.84–86.
- ↑ B. B. Multanovsky. Fundamentals of the synoptic method of long-term weather forecasts. M .: Publishing house TSUEGMS, 1933. — 140 p.
- ↑ Willett HC Patterns of world weather changes // Trans. Amer. Geophys. Union, 1948.— 29. — No 6. — P.803-805.
- ↑ Willett HC Descriptive meteorology. New York: Academic press, 1944. — 310 p.
- ↑ Rossby C. —G., Willett HC The circulation of the upper troposphere and lower stratosphere // Science, 1948.— 108 . —No 2815. — p.643-652.
- ↑ Word F., Shapiro R. Meteorological periodicities // J. Meteorol.— 1961.— 18 .— P.635—656.
- ↑ McGuirk JP, Reiter EP A vacillation of atmospheric energy parameters // J. Atmos. Sci.— 1976.— 33 .— No. 11.— P.2079-2093.
- ↑ Kriegel A.M. On seasonal variability of the duration of the index cycle // Bulletin of the Leningrad State. University. Ser. 7. — 1990. — Issue 1 (No. 7). — S.119-120.
- ↑ Thompson DWJ, Barnes EA Periodic variability in the large-scale Southern hemisphere atmospheric circulation // Science.- 2014.- 343 .— p.641-645.
- ↑ Seidov D.G. Modeling of synoptic and climatic variability of the ocean. L .: Gidrometeoizdat. — 1985. — 207 p.
- ↑ Holland WR, Haidvogel DB On the vacillation of an unstable baroclinic wave field in an eddy-resolving model of the oceanic general circulation // J. Phys. Ocean. — 1981.— 11. — No. 4.
- ↑ Neyelov I.A., Chalikov D.V. Model of mesoscale circulation in the open ocean // Oceanology. — 1981.— 21. — No. 1. — P.5-11.
- ↑ Stommel H. The Gulf Stream. A physical and dynamical description. Univ. of California Press. Berckley. — 1965. — 248 pp.
- ↑ Kriegel A. M., Pigulevsky Yu. V. On the similarity between fluctuations of the index cycle type in the atmosphere and in the ocean // Bulletin of the Leningrad State. University. Ser. 7. — 1990. — issue 4 (No. 28) .— S.95-97.
- ↑ Kriegel A. M. About the similarity between slow fluctuations in the atmospheres of planets and the cycle of solar activity // Bulletin of the Leningrad State. University. Ser. 7.— 1988. — Vol. 3 (No. 21) .— S.122-125.
- ↑ Hide R. Some experiments on thermal convection in a rotating liquid // Quart J. Roy. Meteorol. Soc., 1953.— 79. — No.339.— p. 161.
- ↑ Hide R. An experimental study of thermal convection in a rotating fluid // Phil. Trans. Roy. Soc. London, 1958. — A 250. — P. 441-478.
- ↑ Lorenz EN The mechanics of vacillation // J. Atmos. Sci., 1963. — 20. — P. 448-464.
- Kriegel A. Atmosphere on the verge of order and chaos // Knowledge — power. — 1989. — No. 8. — S.30—35.