Hybrid modeling of the tearing instability in collisionless two-dimensional current sheets: Linear theory

1995 ◽  
Vol 100 (A11) ◽  
pp. 21827-21833 ◽  
Author(s):  
Masha M. Kuznetsova ◽  
Michael Hesse ◽  
Dan Winske
Keyword(s):  
Linear Theory ◽  
Hybrid Modeling ◽  
Two Dimensional ◽  
Current Sheets ◽  
Tearing Instability

A non-linear theory for a full cavitating hydrofoil in a transverse gravity field

1967 ◽  
Vol 29 (2) ◽  
pp. 317-336 ◽  
Author(s):  
Bruce E. Larock ◽  
Robert L. Street
Keyword(s):  
Gravity Field ◽  
Linear Theory ◽  
Mixed Boundary ◽  
Linear Method ◽  
Two Dimensional ◽  
Mixed Boundary Value Problem ◽  
Cavity Model ◽  
Cavity Size ◽  
Non Linear ◽  
Cavitating Hydrofoil

An analysis is made of the effect of a transverse gravity field on a two-dimensional fully cavitating flow past a flat-plate hydrofoil. Under the assumption that the flow is both irrotational and incompressible, a non-linear method is developed by using conformal mapping and the solution to a mixed-boundary-value problem in an auxiliary half plane. A new cavity model, proposed by Tulin (1964a), is employed. The solution to the gravity-affected case was found by iteration; the non-gravity solution was used as the initial trial of a rapidly convergent process. The theory indicates that the lift and cavity size are reduced by the gravity field. Typical results are presented and compared to Parkin's (1957) linear theory.

scholarly journals TSUNAMI GENERATION AND PROPAGATION

1972 ◽  
Vol 1 (13) ◽  
pp. 146
Author(s):  
Joseph L. Hammack ◽  
Frederic Raichlen
Keyword(s):  
Linear Theory ◽  
Source Region ◽  
Three Dimensional ◽  
Frequency Dispersion ◽  
Nonlinear Effects ◽  
Its Region ◽  
Experimental Results ◽  
Specific Class ◽  
Two Dimensional ◽  
Three Dimensional Models

A linear theory is presented for waves generated by an arbitrary bed deformation {in space and time) for a two-dimensional and a three -dimensional fluid domain of uniform depth. The resulting wave profile near the source is computed for both the two and three-dimensional models for a specific class of bed deformations; experimental results are presented for the two-dimensional model. The growth of nonlinear effects during wave propagation in an ocean of uniform depth and the corresponding limitations of the linear theory are investigated. A strategy is presented for determining wave behavior at large distances from the source where linear and nonlinear effects are of equal magnitude. The strategy is based on a matching technique which employs the linear theory in its region of applicability and an equation similar to that of Korteweg and deVries (KdV) in the region where nonlinearities are equal in magnitude to frequency dispersion. Comparison of the theoretical computations with the experimental results indicates that an equation of the KdV type is the proper model of wave behavior at large distances from the source region.

scholarly journals Topological Catastrophe in Massive Current Sheets

1989 ◽  
Vol 104 (2) ◽  
pp. 285-288
Author(s):  
Ph. Peterle ◽  
J. Hoyvaerts
Keyword(s):  
Boundary Conditions ◽  
Mass Flux ◽  
Flux Ratio ◽  
Continuous Variation ◽  
Two Dimensional ◽  
Cusp Point ◽  
Fixed Boundary ◽  
Current Sheets ◽  
Solar Filaments

AbstractA two-dimensional sheet model for solar filaments (Kippenhahn and Schluter configuration) is considered. We investigate, the quasi-static evolution of gravito-magnetohydrostatic equlibria in exploring the response of massive current sheets to a slow continuous variation of the mass/flux ratio with fixed boundary conditions. A catastrophic behavior of the field topology is found to occur in the sequence following the formation of a cusp point (bifurcation).

Effect of plasma-β on the onset of plasmoid instability in Sweet–Parker current sheets

2014 ◽  
Vol 80 (5) ◽  
pp. 655-665 ◽  
Author(s):  
H. Baty
Keyword(s):  
Magnetic Reconnection ◽  
Temperature Increase ◽  
Numerical Study ◽  
Two Dimensional ◽  
Magnetic Island ◽  
Current Sheets ◽  
A Value ◽  
Similar Dependence ◽  
Definition Of ◽  
Local Temperature Increase

AbstractA numerical study of magnetic reconnection in two-dimensional resistive magnetohydrodynamics for Sweet–Parker current sheets that are subject to plasmoid instability is carried out. The effect of the initial upstream plasma-β on the critical Lundquist number Sc for the onset of plasmoid instability is studied. Our results indicate a weak dependence, with a value of Sc ≃ 1.5 × 104 in the limit of zero β, and a value of Sc ≃ 1 × 104 in the opposite high β regime (β ≫ 1). A similar dependence was previously obtained (Ni et al. 2012 Phys. Plasm. 19, 072902), but with a somewhat much larger variation, that can be largely attributed to the different configuration setup used in their study, and also to the definition of the Lundquist number. This conclusion does not depend significantly on the equilibrium used, i.e. both initial configurations with either plasma density or temperature spatial variations lead to very similar results. Finally, we show that the inner plasmoid structure appears as an under-dense hotted magnetic island, with a local temperature increase that is noticeably strengthened for low β cases.

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