Why does the magnetic field of the Earth reverse?

Size: px

Start display at page:

Download "Why does the magnetic field of the Earth reverse?"

Erika Hoover
7 years ago
Views:

1 IMPRS Solar System Seminar June 2002 Dieter Schmitt (Katlenburg-Lindau) Page 1 of 21

2 1. Geomagnetic field >99% of matter in universe is plasma: gas of electrons, ions and neutral particles moving charged particles electric currents magnetic fields basic process magnetic fields everywhere in cosmos: planets, stars, accretion disks, galaxies magnetic field of Earth oldest known magnetic field of a celestial body: compass, Gilbert (1600) Gauss (1838): spherical harmonics, sources in interior, mainly dipolar, B E 0.3 G, B P 0.6 G, tilt 11, offset 450 km 0.07 R E, B D r 3 higher multipoles superposed secular variation westdrift of nonaxisymmetric components of 0.18 /yr pole wobble intensity variations polarity reversals, 10 3 yr yr Page 2 of 21

3 SINT-800 VADM (Guyodo & Valet, 1999) Page 3 of 21

4 Ma Ma Page 4 of 21

5 2. Dynamo theory basics composition of Earth solid inner core, r 1200 km, Fe, Ni fluid outer core, r 3500 km, good electrical conductor, thermal and chemical convection, location of electric currents, which excite the geomagnetic field mantle, poorly conducting; thin crust decay time in core: yr electromagnetic induction: u B j B ( u) self-excitation, dynamo-electrical principle (Siemens 1867) disk dynamo: B u uxb Page 5 of 21

6 homogenous dynamo, complicated flows, induction equation B t = rot (u B η rotb), B differential rotation = B pol + B tor helical convection (Parker 1955) Ω Ω θ Ω Ωcosθ θ Ω Ωcosθ uxω u uxω u Page 6 of 21 u u j B j B

7 theory of mean fields (Steenbeck, Krause & Rädler 1966) B = B + B, u = u + u average: ensemble, azimutal, spatial, temporal B t = rot ( u B + u B η rotb) u B = αb η T rotb α = 1 u (t) rot u (t τ)dτ, η 3 T = 1 3 u (t) u (t τ)dτ η αω-dynamo gradω B pol B tor Page 7 of 21 α dynamo number C = R α R Ω = α 0 R/η T Ω 0 R3 /η T

8 stochastic helicity fluctuations δα of each convective cell α = α 0 (θ) + δα (θ, t) with δα = f rmsf (θ, t) α 0 2Nc sin θ correlation length Rθ c = Rπ/N c, correlation time τ c forcing parameter f 2 rmsθ 2 cτ c back reaction of magnetic field on velocity (u, u ) through Lorentz force, e.g. α(b)-quenching sign of B free Page 8 of 21

9 3. 1D mean-field αω-dynamo model azimuthal averages, B axisym. component of field B = B(θ, t) exp(ikr), B = rot(p e φ ) + T e φ θ R dimensionless αω-dynamo equation ( ) ( ) ( P α/α = 0 P t T C( / θ) sin θ T ) Page 9 of 21 diffusion operator dynamo number C α fluctuations and quenching: α = α 0 (θ, B) + δα (θ, t)

10 mode structure: fundamental mode: monotonous dipole, supercritical, nonlinearly saturated B B t t overtones: dipolar and quadrupolar, oscillatory, decaying B t Page 10 of 21

11 effect of α-fluctuations δα: variation of fundamental mode amplitude B t stochastic excitation of higher modes B t Page 11 of 21

12 4. Numerical results standard case: kr = 0.5, Ccrit = 57.9, C = 100, 3 IMPRS, S, 6/2002 frms = 6.4, θc = π/10, τc = Page 12 of 21 part of much longer run with 500 reversals secular dipole ampl. variation d v = h(a hai)2i/hai rapid reversals with Tr 100 τd JJ II J I

13 reversals through decay of fundamental mode and short-time dominance of oscillating overtones Page 13 of 21

14 variation of stochastic forcing: top: f rms = 5.4 dv 0.07, T r 500 τ D bottom: f rms = 7.4 dv 0.3, T r 35 τ D linear increase of forcing from f rms = dv and T r τ D Page 14 of 21

15 variability / secular variation reversal rate Page 15 of 21

16 5. Theoretical analysis Fokker-Planck equation: expansion of B into unperturbed eigenmodes b i B(θ, t) = a i (t)b i (θ) i a i t = λ ia i + (1 a 2 0 ) N ik a k + k k averaging over fluctuations F ik (t)a k p t = a Sa a Dp 2 p(a) probability distribution of fundamental dipole 2 amplitude a = a 0 drift term S = Λ(1 a 2 )a = du/da determined by dynamo model (supercriticality, nonlinearity) diffusion term D = D 0 a 2 + D 1 (a), D 1 (0) 0 depends on forcing f 2 rmsθ 2 cτ c variation of fundamental mode (F 00, D 0 ) influence of overtones (F 0k, D 1 ) Page 16 of 21

17 bistable oscillator p(a) U(a) a U(a) given by U/ a = S symmetry, central hill, side walls, wells reversals through overtones (D 1 ) reversals fast amplitude distribution p(a) D 1 exp a 0 2SD 1 dx dv, T r f rms dv T r ball in honey, reversal is random process, no specific cause 2 Page 17 of 21

18 6. Comparison with SINT-800 data SINT-800 VADM 3 IMPRS, S, 6/2002 secular VADM variation d v = ± dynamo model y Tr 500τD Page 18 of 21 JJ II J I

19 VADM distribution comparison with dynamo Page 19 of 21

20 7. Diffusion time scale τ D VADM(t) and a(t) are essentially the same absolute time turbulent diffusion time adjust τ D until autocorrelation functions match Page 20 of 21 τ D 10 4 yr

21 Page 21 of 21

SIO 229 Gravity and Geomagnetism: Class Description and Goals

SIO 229 Gravity and Geomagnetism: Class Description and Goals This graduate class provides an introduction to gravity and geomagnetism at a level suitable for advanced non-specialists in geophysics. Topics