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Toroidal Field


A divergenceless field can be partitioned into a toroidal and a poloidal part. This separation is important in geo- and heliophysics, and in particular in dynamo theory and helioseismology. The toroidal field is defined as

 T=-1/(sintheta)partial/(partialphi)u(theta,phi)theta^^+partial/(partialtheta)u(theta,phi)phi^^,

which can additionally be multiplied by a radial weighting function w(r).

This is equivalent to the definition

 T=-w(r)·r^^xdel _(horizontal)u(theta,phi),

where u is a scalar function and the gradient is taken in spherical coordinates.


See also

Divergenceless Field, Poloidal Field

This entry contributed by Lasse Krieger

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References

Krause, F. and Raedler, K.-H. Mean-Field Magnetohydrodynamics and Dynamo Theory. Berlin: Akademie-Verlag, pp. 163 and 167, 1980.Roberts, P. H. An Introduction to Magnetohydrodynamics. New York: American Elsevier, p. 81, 1967.Stacey, F. D. Physics of the Earth, 2nd ed. New York: Wiley, p. 239, 1977.

Referenced on Wolfram|Alpha

Toroidal Field

Cite this as:

Krieger, Lasse. "Toroidal Field." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/ToroidalField.html

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