Abstract The daily sunspot numbers of the whole disk as well as the northern and southern hemispheres from 1945 January 1 to 2010 December 31 are used to investigate the temporal variation of rotational cycle length through the continuous wavelet transformation analysis method. Auto-correlation function analysis of daily hemispheric sunspot numbers shows that the southern hemisphere rotates faster than the northern hemisphere. The results obtained from the wavelet transformation analysis are that no direct relationship exists between the variation trend of the rotational cycle length and the solar activity in the two hemispheres and that the rotational cycle length of both hemispheres has no significant period appearing at 11 yr, but has a significant period of about 7.6 yr. Analysis concerning the solar cycle dependence of the rotational cycle length shows that acceleration seems to appear before the minimum time of solar activity in the whole disk and the northern hemisphere, respectively. Furthermore, the cross-correlation study indicates that the rotational cycle length of the two hemispheres has different phases, and that the rotational cycle length of the whole disk as well as the northern and southern hemispheres, also has phase shifts with corresponding solar activity. In addition, the temporal variation of the north-south (N-S) asymmetry of the rotational cycle length is also studied. This displays the same variation trend as the N-S asymmetry of solar activity in a solar cycle, as well as in the considered time interval, and has two significant periods of 7.7 and 17.5 yr. Moreover, the rotational cycle length and the N-S asymmetry of solar activity are highly correlated. It is inferred that the northern hemisphere should rotate faster at the beginning of solar cycle 24.

Keywords Sun: activity — Sun: rotation — Sun: sunspot

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