An optimal transient growth of small perturbations in thin gaseous discs

A thin gaseous disc with an almost keplerian angular velocity profile, bounded by a free surface and rotating around point-mass gravitating object is nearly spectrally stable. Despite that the substantial transient growth of linear perturbations measured by the evolution of their acoustic energy is possible. This fact is demonstrated for the simple model of a non-viscous polytropic thin disc of a finite radial size where the small adiabatic perturbations are considered as a linear combination of neutral modes with a corotational radius located beyond the outer boundary of the flow.Comment: 15 pages, 5 figures, accepted for publication in Ast

Evolution of unsteady jets in the Rayleigh-Taylor instability

International audienceThe paper concerns the temporal evolution of the Rayleigh-Taylor instability of two superimposed fluids in a vertical channel. At large times the instability results in the formation of a wide nearly-steady bubble of the lighter fluid rising through the channel, and thin long unsteady jets of the heavier fluid flowing down the channel walls. The jet flow appears to be tractable asymptotically by the method of matched expansions. The solution has been obtained with the planar tips of jets characterized by the jump of the interface slope

Generation of intermediately-long sea waves by weakly sheared winds

The present study concerns the numerical modeling of sea-wave instability under the effect of logarithmic-wind profile in hurricane conditions. The central point of the study is the calculation of the wave growth rate, which is proportional to the fractional input energy from the weakly-sheared (logarithmic) wind to the wave exponentially varying with time. It is shown for hurricane conditions that the Miles-type stability model based on the Charnock's formula with the standard constant coefficient underestimates the growth rate ~5 to 50 times as compared with the model employing the roughness adopted from experimental data for hurricane winds. The drag reduction with wind speed at hurricane conditions coupled with the similar behavior of the dimensionless gravity acceleration, leads to the minimum in the maximal growth rate and the maximum in the most unstable wavelength.Comment: This paper has been withdrawn by the author due to misprinting error