Solar internal rotation and dynamo waves: A two-dimensional asymptotic solution in the convection zone

2000 ◽  
Vol 21 (3-4) ◽  
pp. 379-380
Author(s):  
Gaetano Belvedere ◽  
Kirill Kuzanyan ◽  
Dmitry Sokoloff
Keyword(s):  
Asymptotic Solution ◽  
Internal Rotation ◽  
Convection Zone ◽  
Two Dimensional ◽  
Dynamo Waves

Solar Internal Rotation and Dynamo Waves: A Two-Dimensional Asymptotic Solution in the Convection Zone

2000 ◽  
Vol 179 ◽  
pp. 379-380
Author(s):  
Gaetano Belvedere ◽  
Kirill Kuzanyan ◽  
Dmitry Sokoloff
Keyword(s):  
Magnetic Field ◽  
Asymptotic Solution ◽  
Internal Rotation ◽  
Convection Zone ◽  
General Idea ◽  
Dynamo Model ◽  
Axially Symmetric ◽  
Dynamo Action ◽  
Regeneration Rate ◽  
Dynamo Waves

Extended abstractHere we outline how asymptotic models may contribute to the investigation of mean field dynamos applied to the solar convective zone. We calculate here a spatial 2-D structure of the mean magnetic field, adopting real profiles of the solar internal rotation (the Ω-effect) and an extended prescription of the turbulent α-effect. In our model assumptions we do not prescribe any meridional flow that might seriously affect the resulting generated magnetic fields. We do not assume apriori any region or layer as a preferred site for the dynamo action (such as the overshoot zone), but the location of the α- and Ω-effects results in the propagation of dynamo waves deep in the convection zone. We consider an axially symmetric magnetic field dynamo model in a differentially rotating spherical shell. The main assumption, when using asymptotic WKB methods, is that the absolute value of the dynamo number (regeneration rate) |D| is large, i.e., the spatial scale of the solution is small. Following the general idea of an asymptotic solution for dynamo waves (e.g., Kuzanyan & Sokoloff 1995), we search for a solution in the form of a power series with respect to the small parameter |D|–1/3(short wavelength scale). This solution is of the order of magnitude of exp(i|D|1/3S), where S is a scalar function of position.

scholarly journals Regularized Solution of Singularly Perturbed Cauchy Problem in the Presence of Rational “Simple” Turning Point in Two-Dimensional Case

Axioms ◽  
2019 ◽  
Vol 8 (4) ◽  
pp. 124 ◽  
Author(s):  
Alexander Eliseev ◽  
Tatjana Ratnikova
Keyword(s):  
Cauchy Problem ◽  
Asymptotic Solution ◽  
Regularization Method ◽  
Turning Point ◽  
Singularly Perturbed ◽  
Dimensional Case ◽  
Singularly Perturbed Problem ◽  
Two Dimensional ◽  
Limit Operator ◽  
Regularized Solution

By Lomov’s S.A. regularization method, we constructed an asymptotic solution of the singularly perturbed Cauchy problem in a two-dimensional case in the case of violation of stability conditions of the limit-operator spectrum. In particular, the problem with a ”simple” turning point was considered, i.e., one eigenvalue vanishes for t = 0 and has the form t m / n a ( t ) (limit operator is discretely irreversible). The regularization method allows us to construct an asymptotic solution that is uniform over the entire segment [ 0 , T ] , and under additional conditions on the parameters of the singularly perturbed problem and its right-hand side, the exact solution.

scholarly journals The Sun’s Rotation Near the Interface Between its Convective and Radiative Zones: 1986 to 1990

1993 ◽  
Vol 141 ◽  
pp. 545-548
Author(s):  
Philip R. Goode
Keyword(s):  
Magnetic Field ◽  
Internal Rotation ◽  
Convection Zone ◽  
Solar Observatory ◽  
Private Communication ◽  
Solar Oscillation ◽  
Body Rotation ◽  
Solid Body Rotation ◽  
Temporal And Spatial ◽  
The Magnetic Field

The Sun’s rotation rate near the base of its convection zone might be expected to vary over the solar cycle because of related changes there in the magnetic field. Helioseismic analyses have taught us that much of the Sun’s convection zone rotates with surface-like differential rotation and a transition toward solid body rotation beneath. For a review of what we know about the Sun’s internal rotation, see Goode, et al.(1991). We now have sufficient solar oscillation data to look for changes in the internal rotation near the base of the convection zone. The relevant data are from the 1986, 1988, 1989 and 1990 Big Bear Solar Observatory( BBSO) sets, Libbrecht and Woodard(1992, private communication). These four datasets were gathered at the same site for roughly the same number of days, reduced in the same way and span the same temporal and spatial frequency ranges—the differences between the sets should arise primarily because they were obtained in different years.

An Analytical Study of the Standard k–ε Model

1990 ◽  
Vol 112 (2) ◽  
pp. 192-198 ◽  
Author(s):  
N. Takemitsu
Keyword(s):  
Experimental Data ◽  
Asymptotic Solution ◽  
Channel Flow ◽  
Analytical Study ◽  
Turbulent Channel Flow ◽  
Second Order ◽  
Two Dimensional ◽  
Ill Posed ◽  
Leading Term ◽  
Logarithmic Law

An asymptotic solution of the standard k–ε model for two-dimensional turbulent channel flow is found. Using this solution, five model constants in the model are all determined reasonably with the aid of experimental data. If an asymptotic solution with the logarithmic law as the leading term is sought for, the standard k–ε model is shown to be ill-posed since the second-order solution has divergent terms.

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