LARGE-SCALE DISTORTIONS OF SQUARE PATTERNS

1994 ◽  
Vol 04 (05) ◽  
pp. 1147-1154 ◽  
Author(s):  
ALEXANDER NEPOMNYASHCHY
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Large Scale ◽  
Instability Threshold ◽  
Amplitude Equations ◽  
Wave Disturbances ◽  
Long Wave

Stationary square patterns are typical in several instability problems. Near the instability threshold, the evolution of long-wave disturbances can be described by a system of amplitude equations resembling the Newell-Whitehead-Segel equations. These equations are used for the linear stability analysis and the investigation of the defects.

scholarly journals On the porosity influence on stability of flow over porous medium

2020 ◽  
Vol 30 (1) ◽  
pp. 134-144
Author(s):  
K.B. Tsiberkin
Keyword(s):  
Porous Medium ◽  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Short Wave ◽  
Wave Instability ◽  
Plane Parallel ◽  
Long Wave ◽  
The Stability ◽  
Critical Wavenumber

The stability of incompressible fluid plane-parallel flow over a layer of a saturated porous medium is studied. The results of a linear stability analysis are described at different porosity values. The considered system is bounded by solid wall from the porous layer bottom. Top fluid surface is free and rigid. A linear stability analysis of plane-parallel stationary flow is presented. It is realized for parameter area where the neutral stability curves are bimodal. The porosity variation effect on flow stability is considered. It is shown that there is a transition between two main instability modes: long-wave and short-wave. The long-wave instability mechanism is determined by inflection points within the velocity profile. The short-wave instability is due to the large transverse gradient of flow velocity near the interface between liquid and porous medium. Porosity decrease stabilizes the long wave perturbations without significant shift of the critical wavenumber. Simultaneously, the short-wave perturbations destabilize, and their critical wavenumber changes in wide range. When the porosity is less than 0.7, the inertial terms in filtration equation and magnitude of the viscous stress near the interface increase to such an extent that the Kelvin-Helmholtz analogue of instability becomes the dominant mechanism for instability development. The stability band realizes in narrow porosity area. It separates the two branches of the neutral curve.

Instability of flow in a curved alluvial channel

1975 ◽  
Vol 72 (1) ◽  
pp. 145-160 ◽  
Author(s):  
Frank Engelund
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Large Scale ◽  
Alluvial Channels ◽  
Annular Flume ◽  
Scour Holes ◽  
Alluvial Channel

This paper deals with two main problems concerning flow in curved alluvial channels. First, the large-scale bottom geometry that develops through the interaction of flow and sediment motion is determined. Second, experiments in an annular flume indicate that the bed is unstable and that this particular instability leads to the formation of a certain number of scour holes. This is explained by a linear stability analysis.

Linear stability of a two-fluid interface for electrohydrodynamic mixing in a channel

2007 ◽  
Vol 583 ◽  
pp. 347-377 ◽  
Author(s):  
F. LI ◽  
O. OZEN ◽  
N. AUBRY ◽  
D. T. PAPAGEORGIOU ◽  
P. G. PETROPOULOS
Keyword(s):  
Stability Analysis ◽  
Electric Field ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Neutral Stability ◽  
Surface Charges ◽  
Two Fluids ◽  
Long Wave ◽  
Normal Electric Field ◽  
Two Fluid

We study the electrohydrodynamic stability of the interface between two superposed viscous fluids in a channel subjected to a normal electric field. The two fluids can have different densities, viscosities, permittivities and conductivities. The interface allows surface charges, and there exists an electrical tangential shear stress at the interface owing to the finite conductivities of the two fluids. The long-wave linear stability analysis is performed within the generic Orr–Sommerfeld framework for both perfect and leaky dielectrics. In the framework of the long-wave linear stability analysis, the wave speed is expressed in terms of the ratio of viscosities, densities, permittivities and conductivities of the two fluids. For perfect dielectrics, the electric field always has a destabilizing effect, whereas for leaky dielectrics, the electric field can have either a destabilizing or a stabilizing effect depending on the ratios of permittivities and conductivities of the two fluids. In addition, the linear stability analysis for all wavenumbers is carried out numerically using the Chebyshev spectral method, and the various types of neutral stability curves (NSC) obtained are discussed.

Sign in / Sign up

Export Citation Format

Share Document