Browsing by Author "Bhattacharjee, Jayanta K."

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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 transonicity
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.
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 given
Static & dynamic aspects of transonicity in bondi accretion
(2006-11-23) Ray, Arnab K.; Bhattacharjee, Jayanta K.
Transonicity in a spherically symmetric accreting system has been considered in both the stationary and the dynamic regimes. The stationary ﬂow, set up as a dynamical system, has been shown to be greatly unstable to even the minutest possible deviation in the boundary condition for transonicity. With the help of a simple analytical model, and some numerical modelling, it has then been argued that the ﬂow indeed becomes transonic and stable, when the evolution of the ﬂow is followed through time. The time-dependent 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 analog acoustic black hole.