Elementary stratified flows with stability at low Richardson number
Speaker: Dr. Ricardo Barros (Instituto Nacional de Matemática Pura e Aplicada Rio de Janeiro)
Time: 2:00PM
Date: Wednesday, December 18th 2013
Location: Seminar Room (G24), Ground Floor, NexusUCD, University College Dublin. Blocks 9 & 10, Belfield Office Park
Abstract:
By examining the linear stability problem for stratified shear flows with sharp density transitions, we explore the possibility of such flows to be stable at arbitrary low Richardson number. The requirements for such feature to occur will be discussed through three classical physical configurations, for which the dispersion relation can be obtained in closed form as a polynomial in the wave speed. The coefficients involved, however, are too cumbersome to handle, making the task of fully describing the stability features of such physical systems rather challenging. To shed light on these issues we use an alternative approach. In the same spirit of Taylor (1931) and Ovsyannikov (1979, 1985), we propose a geometrical approach consisting in interpreting this polynomial equation in one single variable as a plane algebraic curve. Characterizing the way in which the curve tends to infinity, will be the key ingredient to describe the effects on the stability of the flow when subjected to a large shear.
Series: Applied and Computational Mathematics Seminar Series
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