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THE BASIC PHYSICS OF THE LINEAR TRANSIENT GROWTH IN PLANE SHEAR FLOWS

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The energy transient growth mechanism of linear perturbations in plane constant shear flows is re-examined. Considering fluid particle dynamics and operating in terms of the pressure force, we focus on the physics of the energy exchange between the base flow and a single Kelvin mode (i.e. plane waves or spatial Fourier harmonics of perturbations). The keystone of the energy exchange physics is the elastic reflection of the fluid particles from the maximum pressure plane of the Kelvin mode. An interplay of these physics with the shear flow kinematics quantitatively exactly describes the transient growth and, what is most important, the linear dynamics of the system allows to construct the dynamical equations that are identical to the Euler ones. The proposed mechanism is equally applicable to two- and three-dimensional (2D and 3D) perturbations and, thus, shows the universal nature of the transient growth physics in contrast to the widely accepted explanations, separating 2D (Orr mechanism) and 3D perturbations (lift-up mechanism).

Author(s):

George Chagelisvhili    
Abastumani Astrophysical Observatory, Ilia State University, Tbilisi
Georgia

Jan-Niklas Hau    
Chair of Fluid Dynamics, Department of Mechanical Engineering, TU Darmstadt
Germany

George Khujadze    
Chair of Fluid Dynamics, Department of Mechanical Engineering, TU Darmstadt
Germany

Martin Oberlack    
Chair of Fluid Dynamics, Department of Mechanical Engineering, TU Darmstadt
Germany