scholarly journals Waves of Solar Activity

1991 ◽  
Vol 130 ◽  
pp. 117-128
Author(s):  
M.R.E. Proctor ◽  
E.A. Spiegel

AbstractWe develop a theory of the sunspot cycle predicated on the assumption that the observed bands of activity are packets of dynamo waves. An approximate equation is proposed to describe the dynamics of these packets, using standard ideas from bifurcation theory. We show that in a certain limit the system can be described in terms of a slowly-evolving solitary wave, and that periodic behavior, like that of the observed butterfly diagram, can easily be found. Generalizations of the theory are discussed.

2000 ◽  
Vol 179 ◽  
pp. 163-165
Author(s):  
S. K. Solanki ◽  
M. Fligge ◽  
P. Pulkkinen ◽  
P. Hoyng

AbstractThe records of sunspot number, sunspot areas and sunspot locations gathered over the centuries by various observatories are reanalysed with the aim of finding as yet undiscovered connections between the different parameters of the sunspot cycle and the butterfly diagram. Preliminary results of such interrelationships are presented.


2005 ◽  
Vol 16 (2) ◽  
pp. 239-253 ◽  
Author(s):  
William J. R. Alexander ◽  
William J. R. Emeritus

Statistically significant 21-year periodicity is present concurrently in South African annual rainfall, river flow, flood peak maxima, groundwater levels, lake levels and the Southern Oscillation Index. This is directly related to the double sunspot cycle. The first years of the periodic sequences are characterised by sudden, regular and therefore predictable, reversals from sequences of well below average rainfall and river flow (droughts) that are suddenly broken by sequences of well above average events (floods). These reversals are directly related to corresponding six-fold increases in sunspot activity at this time. The two sunspot cycles that comprise the double sunspot cycle also have fundamentally different effects on the hydrometeorological responses. These observations are solidly based and will require a re-assessment of the nature of the solar activity that gives rise to them.


2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Yongan Xie ◽  
Shengqiang Tang

We study a class of high dispersive cubic-quintic nonlinear Schrödinger equations, which describes the propagation of femtosecond light pulses in a medium that exhibits a parabolic nonlinearity law. Applying bifurcation theory of dynamical systems and the Fan sub-equations method, more types of exact solutions, particularly solitary wave solutions, are obtained for the first time.


1990 ◽  
Vol 43 (3) ◽  
pp. 357 ◽  
Author(s):  
JO Murphy

Initially, the rise and fall components of the ll-year solar sunspot cycle are approximated by separate least-squares polynomials for four cycle classifications, which are determined by the magnitude of the average of the annual sunspot numbers per cycle. Following, a method is formulated to generate detailed reconstruction of the annual variation of a solar cycle based on this cycle average, and the results obtained for cycles -4 through to 21 are compared with the annual Zurich values. This procedure is then employed to establish annual sunspot numbers using published average cycle values obtained from atmospheric carbon 14 variations, which have been derived from the chemical analysis of tree ring sections. The reconstructed sequences are correlated with the observed cycle values and with tree ring width index chronologies which exhibit a significant II-year periodicity. It is anticipated that the long carbon 14 records and parallel dendrochronological data could be employed to obtain a more detailed portrayal of previous periods of strong solar activity than that given by current estimates based on historical records.


Author(s):  
Douglas V. Hoyt ◽  
Kenneth H. Shatten

Until now we have considered only 11-year variations in solar activity and climate. The sun also varies on longer time scales. Since these variations seem to parallel a number of climatic changes, the sun may contribute to climatic changes on time scales of decades to centuries. We now examine several solar indices that vary in parallel with Earth’s climate change. There exist plausible arguments that these indices are proxy indicators of the sun’s radiative output, but there is no proof. We now present the strongest correlations we have seen for a sun/climate connection. First, as it is the most widely publicized index, we consider the mean level of solar activity. In 1801 Herschel first proposed a relationship between climate and the level of solar activity. Second, we examine solar cycle lengths, which have been studied sporadically since 1905. Third, we look at two closely related indices—sunspot structure and sunspot decay rates. Fourth, we consider variations in the solar rotation rate. Lastly, we examine some major solar and climatic events of the last thousand years to see if any indications of solar influence are evident on climate. Although we present the solar-induced changes as arising from total-irradiance variations, as discussed earlier spectral-irradiance changes may be the primary driver. When Rudolf Wolf reconstructed solar activity based on historical observations of sunspots, he found an 11-year cycle going back to at least 1700. In 1853 Wolf also claimed that there is an 83-year sunspot cycle. This longer term variation becomes evident simply by smoothing the data, as in Socher’s 1939 example. Wolf’s original discovery of an 83-year cycle was forgotten, but the long cycle was rediscovered by H. H. Turner, W. Schmidt, H. H. Clayton, and probably others. After W. Gleissberg also discovered this 80- to 90-year cycle around 1938, he published so much material on the subject that ever since it has been called the Gleissberg cycle. All these rediscoveries of the same phenomenon indicate that the 80- to 90-year cycle may be real but not strictly periodic. Rather, the cycle may be a “persistency” with an 80- to 90-year period. During this period solar activity is quite powerful but fails to exhibit a single sharp spectral peak.


2012 ◽  
Vol 252 ◽  
pp. 36-39 ◽  
Author(s):  
Min Sun ◽  
Jing Li ◽  
Ting Ting Quan

In this paper, the peakons and bifurcations in a generalized Camassa-Holm equation are studied by using the bifurcation method and qualitative theory of dynamical systems. First, the averaged equation is obtained by introducing linear transform and traveling wave transform to the generalized Camassa-Holm equation. Then, we applied the bifurcation theory of planar dynamical system and maple software to investigate the averaged equation. The phase portrait of the system under a parameter condition is obtained. Finally, we get the peakons from the limit of general single solitary wave solution.


1972 ◽  
Vol 2 (3) ◽  
pp. 144-146 ◽  
Author(s):  
P. R. Wilson

Despite the success of the Babcock-Leighton model in explaining some phenomena of the solar cycle, e.g. Hale’s polarity law and Maunder’s butterfly diagram, it has recently encountered a number of observational and theoretical difficulties. The observational difficulties are centred around the different behaviour of bi-polar magnetic regions (BMRs) and uni-polar magnetic regions (UMRs). Babcock explains BMRs as the surface eruptions of toroidal fields wound by the differential rotation and it is clear that in their subsequent evolution and decay they are obviously influenced by this effect. However, UMRs display a sector structure in which the boundaries between regions of opposite polarities appear to be quite unaffected by the differential rotation but closely related to the interplanetary field sectors. Another feature of solar activity unexplained by the Babcock theory is the tendency of sunspots, flares, etc. to reappear at the same latitude during a cycle. Warwick has observed that proton flares show a preference for particular latitudes which may extend over several cycles. Again Bumba et al. have observed that new cycle fields tend to appear in longitude regions where old cycle fields are still visible.


2002 ◽  
Vol 12 (02) ◽  
pp. 397-407 ◽  
Author(s):  
ZHENGRONG LIU ◽  
JIBIN LI

Bifurcations of solitary waves and domain wall waves for a KdV-like equation with higher order nonlinearity are studied, by using bifurcation theory of planar dynamical systems. Bifurcation parameter sets are shown. Numbers of solitary waves and domain wall waves are given. Under some parameter conditions, a lot of explicit formulas of solitary wave solutions and domain wall solutions are obtained.


2000 ◽  
Vol 10 (11) ◽  
pp. 2519-2526 ◽  
Author(s):  
MILAN PALUŠ ◽  
JÜRGEN KURTHS ◽  
UDO SCHWARZ ◽  
DAGMAR NOVOTNÁ ◽  
IVANKA CHARVÁTOVÁ

The 300 year record of the yearly sunspot numbers and numerically generated trajectory of the solar inertial motion (SIM) were subjects of a synchronization analysis. Phase synchronization of the sunspot cycle and a fast component of the SIM have been found and confirmed with statistical significance in three epochs (1727–1757, 1802–1832 and 1863–1922) of the entire 1700–1997 record. This result can be considered as a quantitative support for the hypothesis that there is a weak interaction of gravity and solar activity.


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