Spiral Convection Columns: Improved Estimate Of Apparent Rotation Period(=1333.6 yr) Of Earth's Solid Inner Core

Details Spiral Convection Columns: Improved Estimate Of Apparent Rotation Period(=1333.6 yr) Of Earth's Solid Inner Core Spiral Convection Columns: Improved Estimate Of Apparent Rotation Period(=1333.6 yr) Of Earth's Solid Inner Core

Nov 1999

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1999aps..dfd..jd09m&link_type=abstract

American Physical Society, Division of Fluid Dynamics Meeting, November 21-23, 1999 New Orleans, LA, abstract #JD.09

Physics

Fluid Dynamics

Scientific paper

In 1974, an est. was made of turbulence driven rot. period of Earth's inner core(r=R_ic), neglecting forced precession, nutation and assuming core fluid's turbulent differential rot., (T_1c^o)_α, alone drives inner core and has achieved steady state so that viscous boundary condition, Υ_φ(R_ic,θ)=ɛ Υ = Υ_ic - Υ = Υ_φ(R_ic), is closely achieved.^1 Υ is mantle's const. sidereal angular velocity, Υ_ic is inner core's, and Υ_φ(r,θ) is fluid's appar., about Z-axis. In 1st est.^1 we assumed velocity and magnetic modes T_α,P_α and T_β,P_β are stationary random functions of time and deleted classes of modes in simplifying toroidal component eq. of transformed amplification eq.,^2 evaluated for mode (T_2c^o)_β to compute radial function (T_1c^o)_α thru a single integration with respect to r. In making integration we assumed toroidal and poloidal B-field intensities have same radial dependency thru core fluid, R_ic <= r <= 0.9R_c, whereas toroidal mag. field declines monotonely as rarrow 0, where it vanishes. To correct discrepancy, divide T_2c^o(r)_β by f(r) and multiply dr by f(r) and integrate over R_ic,..., R_c; define f(r)=150 gauss × (r/0.9R_c), 0 <= r <= 0.9Rc and f(r)=1500(1-r/R_c) gauss for 0.9Rc <= r <= R_c. Repeating computations^1 gives, for νm = 0.2 × 10^5 esu, rot. period of τ _φ(R_ic)=1768.77 yr, instead of former 812 yr.^1 However, we adopted later Elsasser's 1956 est. electrical conductivity of core fluid, σ = 3 × 10-6 emu, which yields τ_φ=1333.6 yr, as close lower limit since σ continues to increase with depth below mantle's base, R_c. Adopting 0.03 cm sec-1 for upwelling motions we see that spiral motions result that do not influence lifetimes of polar heat sources at Rc but shorten to near 10^3 yr near equator. B_T-,B_P-field replaces turbulance theory to compute τ _φ. ^1 Keith L McDonald, Bul. Am. Phys. Soc., 19(10), 1148, 1974. ^2 K L McDonald, On The Planetary Dynamo Theory, ESSA Tech. Report ERL 64-ESL 3 (Govt. Printing Office, 1968), Eq. 21.

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