Poloidal toroidal decomposition

In vector analysis, a mathematical discipline, a three-dimensional solenoidal vector field F can be considered to be generated by a pair of scalar potentials Ψ and Φ:

: $mathbf\{F\}\; =\; abla\; imes\; Psi\; mathbf\{k\}\; +\; abla\; imes\; (\; abla\; imes\; Phi\; mathbf\{k\})~,$

where k is a unit vector.

This decomposition is analogous to a Helmholtz decomposition, and has been used in dynamo theory.

References

* [http://cdsads.u-strasbg.fr/abs/1984JCoPh..55..461G Numerical simulations of stellar convective dynamos. I — The model and method] , Glatzmaier, G. A.; Journal of Computational Physics, vol. 55, Sept. 1984, pp. 461–484.
* [http://cdsads.u-strasbg.fr/abs/1961hhs..book.....C "Hydrodynamic and hydromagnetic stability"] , Chandrasekhar, Subrahmanyan; International Series of Monographs on Physics, Oxford: Clarendon, 1961, p. 622.
* [http://www.springerlink.com/content/h584m7h23v1k5428/ Decomposition of solenoidal fields into poloidal fields, toroidal fields and the mean flow. Applications to the boussinesq-equations] , Schmitt, B. J. and von Wahl, W; in "The Navier-Stokes Equations II — Theory and Numerical Methods", pp. 291–305; Lecture Notes in Mathematics, Springer Berlin/ Heidelberg, Vol. 1530/ 1992.
* [http://cdsads.u-strasbg.fr/abs/1999ApJS..121..247L Anelastic Magnetohydrodynamic Equations for Modeling Solar and Stellar Convection Zones] , Lantz, S. R. and Fan, Y.; The Astrophysical Journal Supplement Series, Volume 121, Issue 1, Mar. 1999, pp. 247–264.