2007 (IPP)
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Item Standing and travelling waves in the shallow-water circular hydraulic jump(2007-08-20) Ray, Arnab K.; Bhattacharjee, Jayanta K.A wave equation for a time-dependent perturbation about the steady shallow-water solution emulates the metric an acoustic white hole, even upon the incorporation of nonlinearity in the lowest order. A standing wave in the sub-critical region of the flow is stabilised by viscosity, and the resulting time scale for the amplitude decay helps in providing a scaling argument for the formation of the hydraulic jump. A standing wave in the super-critical region, on the other hand, displays an unstable character, which, although somewhat mitigated by viscosity, needs nonlinear effects to be saturated. A travelling wave moving upstream from the sub-critical region, destabilises the flow in the vicinity of the jump, for which experimental support has been givenItem Secular instability in quasi-viscous disc accretion(2007-07-12) Bhattacharjee, Jayanta K.; Ray, Arnab K.A first-order correction in the -viscosity parameter of Shakura& Sunyaev has been introduced in the standard inviscid and thin accretion disc. A linearised time-dependent perturbative study of the stationary solutions of this “quasi-viscous” disc leads to the development of a secular instability on large spatial scales. This qualitative feature is equally manifest for two different types of perturbative treatment — a standing wave on subsonic scales, as well as a radially propagating wave. Stability of the flow is restored when viscosity disappears.Item Evolution of transonicity in an accretion disc(2007-01-10) Ray, Arnab K.; Bhattacharjee, Jayanta K.For inviscid, rotational accretion ows driven by a general pseudo Newtonian potential on to a Schwarzschild black hole, the only possible xed points are saddle points and centre-type points. For the speci c choice of the Newtonian potential, the ow has only two critical points, of which the outer one is a saddle point while the inner one is a centre-type point. A restrictive upper bound is imposed on the admissible range of values of the angular momentum of sub-Keplerian ows through a saddle point. These ows are very unstable to any deviation from a necessarily precise boundary condition. The di culties against the physical realisability of a solution passing through the saddle point have been addressed through a temporal evolution of the ow, which gives a non-perturbative mechanism for selecting a transonic solution passing through the saddle point. An equation of motion for a real-time perturbation about the stationary ows reveals a very close correspondence with the metric of an acoustic black hole, which is also an indication of the primacy of transonicityItem 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.Item Critical properties of spherically symmetric accretion in a fractal medium(2007-07-18) Roy, Nirupam; Ray, Arnab K.Spherically symmetric transonic accretion of a fractal medium has been studied in both the stationary and the dynamic regimes. The stationary transonic solution is greatly sensitive to infinitesimal deviations in the outer boundary condition, but the flow becomes transonic and stable, when its evolution is followed through time. The evolution towards transonicity is more pronounced for a fractal medium than what is it for a continuum. The dynamic approach also shows that there is a remarkable closeness between an equation of motion for a perturbation in the flow, and the metric of an analogue acoustic black hole. The stationary inflow solutions of a fractal medium are as much stable under the influence of linearised perturbations, as they are for the fluid continuum.Item 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.Item Acoustic perturbations on steady spherical accretion in Schwarzschild geometry(2007-06-10) Naskar, Tapan; Ray, Arnab K.The stationary background flow in the spherically symmetric infall of a compressible fluid, coupled to the space-time defined by the static chwarzschild metric, has been subjected to linearized acoustic perturbations. The perturbative procedure is based on the continuity condition and it shows that the coupling of the flow with the geometry of space-time brings about greater stability for the flow, to the extent that the amplitude of the perturbation, treated as a standing wave, decays in time, as opposed to the amplitude remaining constant in the Newtonian limit. In ualitative terms this situation simulates the effect of a dissipative mechanism in the classical Bondi accretion flow, defined in the Newtonian construct of space and time. As a result of this approach it becomes impossible to define an acoustic metric for a conserved spherically symmetric flow, described within the framework of Schwarzschild geometry. In keeping with this view, the perturbation, considered eparately as a high-frequency travelling wave, also has its amplitude reduced.