1 / 7

Modeling of the solar interface dynamo

Modeling of the solar interface dynamo. Vienna, EGU-2012. Artyushkova M. E. Schmidt Institute of Physics of the Earth of the Russian Academy of Sciences.

norah
Download Presentation

Modeling of the solar interface dynamo

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Modeling of the solar interface dynamo Vienna, EGU-2012 Artyushkova M. E. Schmidt Institute of Physics of the Earth of the Russian Academy of Sciences Based on “Popova H., Artyushkova M. and Sokoloff D. The WKB approximation for the interface dynamo // Geophysical & Astrophysical Fluid Dynamics. 2010. V.104, № 5. P. 631-641.“

  2. Single-layer dynamo model proposed by Parker in 1955. Parker, E.N., Hydromagnetic dynamo models// Astrophysical Journal. 1955, 122, 293–314. • toroidalmagnetic field • toroidal component ofvectorial potential, • poloidal magnetic field • latitude (so corresponds to the poles). • dynamo number combined with α-effectamplitude, differential rotationΩ • and coefficient of diffusion. So the equation system is dimensionless.

  3. WKB-approach for solving migratory dynamo model Kuzanyan, K.M. and Sokoloff, D.D., A dynamo wave in an inhomogeneous medium. Geophys. Astrophys.Fluid Dyn. 1995, 81, 113–129. Bassom, A.P., Kuzanyan, K.M., Sokoloff, D. and Soward, A.M., Non-axisymmetric 2-dynamo waves inthin stellar shells// Geophys. Astrophys. Fluid Dyn. 2005, 2, 309–336. The WKB solution is looked for in the form of waves traveling in the -direction~ where action corresponds tothe wave vector, or impulse - complex growth rate, gives the length of the activity cycle derived from the Hamilton-Jacobi equation According this method the solution must decay towards theboundaries of the domain - the poles and equator

  4. Two-layers dynamo model Parker’s system of equations: Boundary conditions for α-effect localized first layer and the differential rotation Ωlocalized in the second layer • magnetic field, potential in the first layer -magnetic field, potential in the second layer ratio of the turbulent diffusivity coefficients in the first and second layers • dynamo number combined with • α-effect amplitude, Ω

  5. Applying the WKB-approach for two-layers model slowly varying functions The Hamilton–Jacobi equation • Hamilton–Jacobi equation for one-layer dynamo • for comparison

  6. Squared the Hamilton–Jacobi equationwith where Solving the Hamilton–Jacobi equation condition that k has to be continuous from pole to equator, particulary k has to be continuousat a turningpoint, wheretwo roots of the Hamilton–Jacobi equation coincide

  7. Roots of the Hamilton–Jacobi equation for various values of as points in the complexk plane Two-layers model, Single-layer model (Kuzanyan, K.M. and Sokoloff, D.D, 1995) Im {k} Re {k} Numbers 1,2,3,4 enumerate the branchesof the various roots.

More Related