2007 (IPP)
Permanent URI for this collectionhttp://localhost:4000/handle/11007/334
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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 transonicity