A Weakly Nonlinear Stability Analysis of the Reactive Infiltration Interface

1988 ◽  
Vol 48 (6) ◽  
pp. 1362-1378 ◽  
Author(s):  
J. Chadam ◽  
P. Ortoleva ◽  
A. Sen
Keyword(s):  
Stability Analysis ◽  
Nonlinear Stability ◽  
Nonlinear Stability Analysis ◽  
Weakly Nonlinear ◽  
Reactive Infiltration

Spatio-temporal structure of the ‘fully developed’ transitional flow in a symmetric wavy channel. Linear and weakly nonlinear stability analysis

2014 ◽  
Vol 764 ◽  
pp. 250-276 ◽  
Author(s):  
S. Blancher ◽  
Y. Le Guer ◽  
K. El Omari
Keyword(s):  
Stability Analysis ◽  
Laminar Flow ◽  
Steady Flow ◽  
Nonlinear Stability ◽  
Temporal Structure ◽  
Main Stream ◽  
Nonlinear Stability Analysis ◽  
Wavy Channel ◽  
Weakly Nonlinear ◽  
Spatio Temporal

AbstractThis work addresses the transition from 2D steady to 2D unsteady laminar flow for a fully developed regime in a symmetric wavy channel geometry. We investigate the existence and characteristics of the spatio-temporal structure of the fully developed unsteady laminar flow for those particular geometries for which the steady flow presents a periodic variation of the main stream velocity component. We perform a 2D global linear stability analysis of the fully developed steady laminar flow, and we show that, for all the geometries studied, the transition is triggered by a Hopf bifurcation associated with the breaking of the symmetries and the invariance of the steady flow. Critical Reynolds numbers, most unstable modes and their characteristics are presented for large ranges of the geometric parameters, namely wavenumber${\it\alpha}$from 0.3 to 5 and amplitude from 0 (straight channel) to 0.5. We show that it is possible to define geometries for which the wavenumber is proportional to the most unstable mode wavenumber for the critical Reynolds number. From this modal study we address a weakly nonlinear stability analysis with a view to obtaining the Landau coefficient$g$, and then the sub- or supercritical nature of the first bifurcation characterising the transition. We show that a critical geometric amplitude beyond which the first bifurcation is supercritical is associated with each geometric wavenumber.

Nonlinear Stability Analysis of the Thin Micropolar Liquid Film Flowing Down on a Vertical Cylinder

2000 ◽  
Vol 123 (2) ◽  
pp. 411-421 ◽  
Author(s):  
Po-Jen Cheng ◽  
Cha’o-Kuang Chen ◽  
Hsin-Yi Lai
Keyword(s):  
Stability Analysis ◽  
Liquid Film ◽  
Nonlinear Stability ◽  
Film Flow ◽  
Multiple Scales ◽  
Vertical Cylinder ◽  
Nonlinear Stability Analysis ◽  
Weakly Nonlinear ◽  
Free Film ◽  
Micropolar Liquid

This paper investigates the weakly nonlinear stability theory of a thin micropolar liquid film flowing down along the outside surface of a vertical cylinder. The long-wave perturbation method is employed to solve for generalized nonlinear kinematic equations with free film interface. The normal mode approach is first used to compute the linear stability solution for the film flow. The method of multiple scales is then used to obtain the weak nonlinear dynamics of the film flow for stability analysis. The modeling results indicate that both subcritical instability and supercritical stability conditions are possible to occur in a micropolar film flow system. The degree of instability in the film flow is further intensified by the lateral curvature of cylinder. This is somewhat different from that of the planar flow. The modeling results also indicate that by increasing the micropolar parameter K=κ/μ and increasing the radius of the cylinder the film flow can become relatively more stable traveling down along the vertical cylinder.

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