Helicity fluctuations in mean field theory: an explanation for the variability of the solar cycle?

Details Helicity fluctuations in mean field theory: an explanation for the variability of the solar cycle? Helicity fluctuations in mean field theory: an explanation for the variability of the solar cycle?

May 1993

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993a%26a...272..321h&link_type=abstract

Astronomy and Astrophysics, Vol. 272, p. 321 (1993)

Astronomy and Astrophysics

Astrophysics

66

Chaotic Phenomena, Mhd, Turbulence, Methods: Statistical, Sun: Activity, Sun: Magnetic Fields

Scientific paper

We consider the effect of fluctuations δα(t) in the mean helicity α0 (both assumed independent of position) on a plane dynamo wave. The time scale τc of the fluctuations is much shorter than the diffusion time 1/β0κ2(β0κ2τc ≪ 1; β0 = turbulent diffusion coefficient; κ = wave number). We distinguish weak and strong random forcing, according to whether (δαr.m.s./α0)√β0κ2τc is small or large with respect to 1, and we present a detailed analysis of the weak forcing case.
Simple equations are derived for the phases and the logarithmic amplitudes of the poloidal and toroidal mean field, in which the forcing terms appear as additive noise. Phase difference and amplitude ratio of the poloidal and toroidal (mean) field are subject to small fluctuations of constant r.m.s. magnitude. Simple expressions are derived for the r.m.s. phase shift, amplitude drift and quality factor of the toroidal (mean) field. These depend on the fluctuations only through the quantity D = ¼( δαr.m.s./α0)2β0κ2τc which plays the role of a diffusion coefficient. The results are: (1). Phase shift Δ and logarithmic amplitude Λ each perform a random walk; (2). In the α2-limit these random walks are uncorrelated; the phase is very stable but the amplitude is completely irregular; (3). In the αω-limit there exists a correlation: Λ + Δ ≃ 0, which persists for many dynamo periods. The quality factor is then given by Q = 1/D.
The model is then applied to the solar dynamo. The predicted correlation Λ + Δ ≃ 0 implies that weaker (stronger) cycles last longer (shorter) than average, which is a well-known observed feature of the solar cycle. We define Λ and Δ using the epochs of solar maxima and the sunspot numbers, and show that Λ + Δ ≃ 0 is obeyed rather well. This indicates that fluctuations in the mean helicity are an important mechanism causing the observed phase and amplitude variations of the solar cycle. Simulations show many features also seen in the solar cycle, such as quasi-periodicity, intermittency and long periods of low activity. Further inferences are: (1). The sunspot numbers appear to be proportional to the strength of the toroidal field; (2). The quality factor Q is about 10, which makes the solar dynamo a border-line case between weak and strong forcing; (3). The solar data indicate that it is necessary to allow for nonlinear effects; (4). The mean helicity fluctuations δα(t) are caused by very large spatial fluctuations in the local helicity. This could explain the discrepancy between theoretical estimates for α0 and values derived from mean field models.

Affiliated with

Also associated with

No associations

Rating

Helicity fluctuations in mean field theory: an explanation for the variability of the solar cycle? does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Helicity fluctuations in mean field theory: an explanation for the variability of the solar cycle?, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Helicity fluctuations in mean field theory: an explanation for the variability of the solar cycle? will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-1845701