Open AccessPROBLEMS OF THERMAL INSTABILITY IN A SPHERE
Author(s) -
Jeffreys Harold
Publication year - 1952
Publication title -
geophysical journal international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0956-540X
DOI - 10.1111/j.1365-246x.1952.tb03014.x
Subject(s) - instability , radius , spherical harmonics , thermal , mechanics , physics , degree (music) , core (optical fiber) , classical mechanics , analogy , harmonic , harmonics , point (geometry) , geometry , mathematics , thermodynamics , optics , quantum mechanics , linguistics , philosophy , computer security , voltage , computer science , acoustics
Summary The theory of thermal instability in a sphere is extended to the case of a viscous sphere with a fluid core, the radius of the core being half that of the outer surface. The easiest mode to excite no longer corresponds to a spherical harmonic of degree I in the temperature but probably to degree 3 or 4. A more satisfactory model from the petrological point of view is based on the idea of a magma percolating through a mass of incompletely consolidated crystals. Results are obtained for this case, both for a uniform sphere and for one with a core. The harmonics of degree I are not the easiest to excite in either case. From analogy with other hydrodynamical problems it does not appear that these results offer any objection to the theory of the origin of the land and water hemispheres by thermal instability. The essential point is that, given sufficient time, the most widespread disturbances will become dominant provided only that they can be excited at all, and this condition is satisfied in all cases.