Linear dynamics of perturbations in shear flows

Author: Elene Miliukovi
Keywords: shear flow, instability, transient growth, turbulence
Annotation:

Linear dynamics of perturbations in a constant shear flow of incompressible fluid, which is spectrally/modally stable, is investigated. This type of flow is ubiquitous in laboratory, in the atmosphere and ocean as well as in a variety of astrophysical objects, so their stability analysis is of paramount importance in understanding dynamics and evolution of these flows. By linearizing equations of hydrodynamics, we obtain evolution equations for small perturbations. For the analysis we employ a special type of nonmodal approach – Kelvin mode formalism. Then, using numerical integration, we analyze time-evolution of spatial Fourier harmonics and show that they undergo algebraic transient growth (transient instability). We characterize such transient amplificion as a function of two (vertical and streamwise) wavenumbers of harmonics. We discuss implications of our results for laboratory and astrophysical plasma flows, in particular, the role of the transient instability in the onset and maintenance of subcritical turbulence in these flows.

Lecture files:

შეშფოთებათა წრფივი დინამიკა წანაცვლებით დინებებში [ka]