Experimental validation of inviscid linear stability theory applied to an axisymmetric jet

2022 ◽  
Vol 934 ◽  
Author(s):  
L.R. Gareev ◽  
J.S. Zayko ◽  
A.D. Chicherina ◽  
V.V. Trifonov ◽  
A.I. Reshmin ◽  
...  
Keyword(s):  
Linear Stability ◽  
Stability Theory ◽  
Theoretical Calculations ◽  
Linear Stability Theory ◽  
Round Cross Section ◽  
Laminar Jet ◽  
Air Jet ◽  
Inflection Points ◽  
Round Cross ◽  
Axisymmetric Perturbations

We study the development of perturbations in a submerged air jet with a round cross-section and a long laminar region (five jet diameters) at a Reynolds number of 5400 by both inviscid linear stability theory and experiments. The theoretical analysis shows that there are two modes of growing axisymmetric perturbations, which are generated by three generalized inflection points of the jet's velocity profile. To validate the results of linear stability theory, we conduct experiments with controlled axisymmetric perturbations to the jet. The characteristics of growing waves are obtained by visualization, thermoanemometer measurements and correlation analysis. Experimentally measured wavelengths, growth rates and spatial distributions of velocity fluctuations for both growing modes are in good agreement with theoretical calculations. Therefore, it is demonstrated that small perturbations to the laminar jet closely follow the predictions of inviscid linear stability theory.

scholarly journals Convolutional neural network for transition modeling based on linear stability theory

2020 ◽  
Vol 5 (11) ◽  
Author(s):  
Muhammad I. Zafar ◽  
Heng Xiao ◽  
Meelan M. Choudhari ◽  
Fei Li ◽  
Chau-Lyan Chang ◽  
...  
Keyword(s):  
Neural Network ◽  
Convolutional Neural Network ◽  
Linear Stability ◽  
Stability Theory ◽  
Linear Stability Theory ◽  
Transition Modeling

On the linear stability theory of Bénard–Marangoni convection

1989 ◽  
Vol 1 (7) ◽  
pp. 1123-1127 ◽  
Author(s):  
Rafael D. Benguria ◽  
M. Cristina Depassier
Keyword(s):  
Linear Stability ◽  
Stability Theory ◽  
Marangoni Convection ◽  
Linear Stability Theory

scholarly journals Films over topography: from creeping flow to linear stability, theory and experiments, a review

2018 ◽  
Vol 229 (4) ◽  
pp. 1451-1451
Author(s):  
H. Irschik ◽  
M. Krommer ◽  
C. Marchioli ◽  
G. J. Weng ◽  
M. Ostoja-Starzewski
Keyword(s):  
Linear Stability ◽  
Stability Theory ◽  
Creeping Flow ◽  
Linear Stability Theory ◽  
Theory And Experiments

Stability of the Prandtl model for katabatic slope flows

2019 ◽  
Vol 865 ◽  
Author(s):  
Cheng-Nian Xiao ◽  
Inanc Senocak
Keyword(s):  
Linear Stability ◽  
Stability Theory ◽  
Slope Angle ◽  
Transverse Mode ◽  
Base Flow ◽  
Linear Stability Theory ◽  
Vortical Flow ◽  
Longitudinal Modes ◽  
Prandtl Model ◽  
The Stability

We investigate the stability of the Prandtl model for katabatic slope flows using both linear stability theory and direct numerical simulations. Starting from Prandtl’s analytical solution for uniformly cooled laminar slope flows, we use linear stability theory to identify the onset of instability and features of the most unstable modes. Our results show that the Prandtl model for parallel katabatic slope flows is prone to transverse and longitudinal modes of instability. The transverse mode of instability manifests itself as stationary vortical flow structures aligned in the along-slope direction, whereas the longitudinal mode of instability emerges as waves propagating in the base-flow direction. Beyond the stability limits, these two modes of instability coexist and form a complex flow structure crisscrossing the plane of flow. The emergence of a particular form of these instabilities depends strongly on three dimensionless parameters, which are the slope angle, the Prandtl number and a newly introduced stratification perturbation parameter, which is proportional to the relative importance of the disturbance to the background stratification due to the imposed surface buoyancy flux. We demonstrate that when this parameter is sufficiently large, then the stabilising effect of the background stratification can be overcome. For shallow slopes, the transverse mode of instability emerges despite meeting the Miles–Howard stability criterion of $Ri>0.25$. At steep slope angles, slope flow can remain linearly stable despite attaining Richardson numbers as low as $3\times 10^{-3}$.

scholarly journals Decomposition of the temporal growth rate in linear instability of compressible gas flows

2015 ◽  
Vol 778 ◽  
pp. 120-132 ◽  
Author(s):  
Mario Weder ◽  
Michael Gloor ◽  
Leonhard Kleiser
Keyword(s):  
Growth Rate ◽  
Energy Balance ◽  
Linear Stability ◽  
Couette Flow ◽  
Stability Theory ◽  
Compressible Flows ◽  
Linear Instability ◽  
Linear Stability Theory ◽  
Gas Flows ◽  
Temporal Growth Rate

We present a decomposition of the temporal growth rate ${\it\omega}_{i}$ which characterises the evolution of wave-like disturbances in linear stability theory for compressible flows. The decomposition is based on the disturbance energy balance by Chu (Acta Mech., vol. 1 (3), 1965, pp. 215–234) and provides terms for production, dissipation and flux of energy as components of ${\it\omega}_{i}$. The inclusion of flux terms makes our formulation applicable to unconfined flows and flows with permeable or vibrating boundaries. The decomposition sheds light on the fundamental mechanisms determining temporal growth or decay of disturbances. The additional insights gained by the proposed approach are demonstrated by an investigation of two model flows, namely compressible Couette flow and a plane compressible jet.

Sign in / Sign up

Export Citation Format

Share Document