2007 (IPP)

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    Kinetic and magnetic alpha effects in nonlinear dynamo theory
    (2007-01-19) Sur, Sharanya; Subramanian, Kandaswamy; Brandenburg, Axel
    The backreaction of the Lorentz force on the α-effect is studied in the limit of small magnetic and fluid Reynolds numbers, using the first order smoothing approximation (FOSA) to solve both the induction and momentum equations. Both steady and time dependent forcings are considered. In the low Reynolds number limit, the velocity and magnetic fields can be expressed explicitly in terms of the forcing function. The nonlinear α-effect is then shown to be expressible in several equivalent forms in agreement with formalisms that are used in various closure schemes. On the one hand, one can express α completely in terms of the helical properties of the velocity field as in traditional FOSA, or, alternatively, as the sum of two terms, a so-called kinetic α-effect and an oppositely signed term proportional to the helical part of the small scale magnetic field. These results hold for both steady and time dependent forcing at arbitrary strength of the mean field. In addition, the τ-approximation is considered in the limit of small fluid and magnetic Reynolds numbers. In this limit, the τ closure term is absent and the viscous and resistive terms must be fully included. The underlying equations are then identical to those used under FOSA, but they reveal interesting differences between the steady and time dependent forcing. For steady forcing, the correlation between the forcing function and the small-scale magnetic field turns out to contribute in a crucial manner to determine the net α-effect. However for delta-correlated time-dependent forcing, this force–field correlation vanishes, enabling one to write α exactly as the sum of kinetic and magnetic α-effects, similar to what one obtains also in the large Reynolds number regime in theτ-approximation closure hypothesis. In the limit of strong imposed fields, B0, we find α ∝ B−2 0 for delta-correlated forcing, in contrast to the well-known α ∝ B−3 0 behaviour for the case of a steady forcing. The analysis presented here is also shown to be in agreement with numerical simulations of steady as well as random helical flows.
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    Critical properties of spherically symmetric black hole accretion in Schwarzschild geometry
    (2007-02-28) Mandal, Ipsita; Ray, Arnab K.; Das, Tapas K.
    The stationary spherically symmetric accretion flow in the Schwarzschild metric has been set up as an autonomous first-order dynamical system, and it has been studied completely analytically. Of the three possible critical points in the flow, the one that is physically realistic behaves like the saddle point of the standard Bondi accretion problem. One of the two remaining critical points exhibits the strange mathematical behaviour of being either a saddle point or a centre-type point, depending on the values of the flow parameters. The third critical point is always unphysical and behaves like a centre-type point. The treatment has been extended to pseudo-Schwarzschild flows for comparison with the general relativistic analysis.
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    Axisymmetric black hole accretion in the Kerr metric as an autonomous dynamical system
    (2007-02-07) Goswami, Sanghamitra; Khan, Saba Nashreen; Ray, Arnab K.; et al.
    In a stationary, general relativistic, axisymmetric, inviscid and rotational accretion flow, described within the Kerr geometric framework, transonicity has been examined by setting up the governing equations of the flow as a first-order autonomous dynamical system. The consequent linearised analysis of the critical points of the flow leads to a comprehensive mathematical prescription for classifying these points, showing that the only possibilities are saddle points and centre-type points for all ranges of values of the fixed flow parameters. The spin parameter of the black hole influences the multitransonic character of the flow, as well as some of its specific critical properties. The special case of a flow in the space-time of a non-rotating black hole, characterised by the Schwarzschild metric, has also been studied for comparison and the conclusions are compatible with what has been seen for the Kerr geometric case.