Browsing by Author "Timoshin, Sergei"

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    Linear stability of ice growth under a gravity-driven water film
    (American Institute of Physics (AIP), 2006-07) Shapiro, Evgeniy; Timoshin, Sergei
    In this paper we consider linear stability of ice growth under a gravity-driven water film on a sloping wall. First, we derive an analytic solution of the stability problem in the long-wave limit, which shows that the presence of the ice layer generates an additional wave mode. Further, using a long-wave solution as an initial guess, we find the additional wave mode in the numerical solution of the complete Orr-Sommerfeld problem and investigate its behavior numerically for a wide range of problem parameters. We show that the ice mode can become unstable even at moderate Reynolds numbers, and that the ice layer alters the behavior of the mode corresponding to the waves on the liquid film surface. We also demonstrate that the presence of the ice layer stabilizes wave disturbances on the water surface and that, depending on the angle of the incline, the critical Reynolds number of the surface mode can be either increased or decreased.
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    On ice-induced instability in free-surface flows.
    (Cambridge University Press, 2007-04) Shapiro, Evgeniy; Timoshin, Sergei
    The problem of stability of a water-coated ice layer is investigated for a free-surface flow of a thin water film down an inclined plane. An asymptotic (double-deck) theory is developed for a flow with large Reynolds and Froude numbers which is then used to investigate linear two-dimensional, three-dimensional and nonlinear two-dimensional stability characteristics. A new mode of upstream-propagating instability arising from the interaction of the ice surface with the flow is discovered and its properties are investigated. In the linear limit, closed-form expressions for the dispersion relation and neutral curves are obtained for the case of Pr = 1. For the general case, the linear stability problem is solved numerically and the applicability of the solution with Pr = 1 is analysed. Nonlinear double-deck equations are solved with a novel global-marching-type scheme and the effects of nonlinearity are investigated. An explanation of the physical mechanism leading to the upstream propagation of instability waves is provided.
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    On the patterns of interaction between shear and interfacial modes in plane air–water Poiseuille flow
    (The Royal Society, 2005-05-08) Shapiro, Evgeniy; Timoshin, Sergei
    The current work deals with the numerical analysis of linear stability problems in a stratified plain Poiseuille flow of air over water with equal layer heights. The interaction and branch exchange between Tollmien–Schlichting instability in air and interfacial instability is discovered and investigated. This effect is shown to stabilize disturbances with wavelengths of the order of channel height for interfacial waves and to produce a closed stable region inside the neutral curve of the interfacial mode. The behaviour of three unstable modes in the problem, corresponding to Tollmien–Schlichting type instability in air and water layers and interfacial instability respectively, has been studied in detail. Neutral conditions for all three modes and the stable region have been calculated.