Stability of Convection in a Vibrating Porous Layer

Volume 1 ◽  
2004 ◽  
Author(s):  
S. Govender
Keyword(s):  
Gravitational Field ◽  
Linear Stability ◽  
Porous Layer ◽  
Stability Theory ◽  
Linear Stability Theory ◽  
Amplitude Vibration ◽  
Constant Part ◽  
Low Amplitude ◽  
Stability Results

The linear stability theory is used to investigate analytically the effects of vibration on convection in a homogenous porous layer heated from below. The gravitational field consists of a constant part and a sinusoidally varying part, which is tantamount to a vertically oscillating porous layer subjected to constant gravity. The linear stability results are presented for the specific case of low amplitude vibration for which it is shown that increasing the frequency of vibration stabilizes the convection.

On the Possibility of Destabilising Convection in a Gravity Modulated Porous Layer Heated From Above

2004 ◽  
Author(s):  
S. Govender
Keyword(s):  
Linear Stability ◽  
Density Gradient ◽  
Porous Layer ◽  
Stability Theory ◽  
Linear Stability Theory

The linear stability theory is used to investigate analytically the possibility of destabilising convection in a porous layer heated from above and subjected to vibration. The linear stability theory shows that there exists a bandwidth of frequencies for which convection in a porous layer, with a stable density gradient, can be destabilized.

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 $3\times 10^{-3}$.

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