Next Article in Journal
Extraction of Tangential Momentum and Normal Energy Accommodation Coefficients by Comparing Variational Solutions of the Boltzmann Equation with Experiments on Thermal Creep Gas Flow in Microchannels
Next Article in Special Issue
Volume Transport by a 3D Quasigeostrophic Heton
Previous Article in Journal
Thrust Vectoring of a Fixed Axisymmetric Supersonic Nozzle Using the Shock-Vector Control Method
Previous Article in Special Issue
Instability of Lenticular Vortices: Results from Laboratory Experiments, Linear Stability Analysis and Numerical Simulations
Article

Linear Non-Modal Growth of Planar Perturbations in a Layered Couette Flow

Laboratory of Meteorology and Climatology, Department of Physics, University of Ioannina, 45110 Ioannina, Greece
*
Author to whom correspondence should be addressed.
Academic Editor: Xavier Carton
Fluids 2021, 6(12), 442; https://doi.org/10.3390/fluids6120442
Received: 11 November 2021 / Revised: 1 December 2021 / Accepted: 2 December 2021 / Published: 8 December 2021
(This article belongs to the Special Issue Instabilities and Nonlinear Dynamics in Oceanic Flows)
Layered flows that are commonly observed in stratified turbulence are susceptible to the Taylor–Caulfield Instability. While the modal stability properties of layered shear flows have been examined, the non-modal growth of perturbations has not been investigated. In this work, the tools of Generalized Stability Theory are utilized to study linear transient growth within a finite time interval of two-dimensional perturbations in an inviscid, three-layer constant shear flow under the Boussinesq approximation. It is found that, for low optimization times, small-scale perturbations utilize the Orr mechanism and achieve growth equal to that in the case of an unstratified flow. For larger optimization times, transient growth is much larger compared to growth for an unstratified flow as the Kelvin–Orr waves comprising the continuous spectrum of the dynamical operator and the gravity edge-waves comprising the discrete spectrum interact synergistically. Maximum growth is obtained for perturbations with scales within the region of instability, but significant growth is maintained for modally stable perturbations as well. For perturbations with scales within the unstable region, the unstable normal modes are excited at high amplitude by their bi-orthogonals. For perturbations with modally stable scales, the Orr mechanism is utilized to excite at high amplitude neutral propagating waves resembling the neutral Taylor–Caulfield modes. View Full-Text
Keywords: Taylor–Caulfield Instability; layered flows; non-modal growth; optimal perturbations; Orr mechanism Taylor–Caulfield Instability; layered flows; non-modal growth; optimal perturbations; Orr mechanism
Show Figures

Figure 1

MDPI and ACS Style

Iliakis, E.G.; Bakas, N.A. Linear Non-Modal Growth of Planar Perturbations in a Layered Couette Flow. Fluids 2021, 6, 442. https://doi.org/10.3390/fluids6120442

AMA Style

Iliakis EG, Bakas NA. Linear Non-Modal Growth of Planar Perturbations in a Layered Couette Flow. Fluids. 2021; 6(12):442. https://doi.org/10.3390/fluids6120442

Chicago/Turabian Style

Iliakis, Emmanouil G., and Nikolaos A. Bakas. 2021. "Linear Non-Modal Growth of Planar Perturbations in a Layered Couette Flow" Fluids 6, no. 12: 442. https://doi.org/10.3390/fluids6120442

Find Other Styles
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Back to TopTop