Weakly nonlinear stability of Hartmann boundary layers

2003 ◽  
Vol 22 (4) ◽  
pp. 345-353 ◽  
Author(s):  
P. Moresco ◽  
T. Alboussière
Keyword(s):  
Boundary Layers ◽  
Nonlinear Stability ◽  
Weakly Nonlinear

The Linear and Weakly-Nonlinear Stability of a Core Annular Flow in a Corrugated Tube

2000 ◽  
Author(s):  
Hsien-Hung Wei ◽  
David S. Rumschitzki
Keyword(s):  
Thin Film ◽  
Nonlinear Stability ◽  
Annular Flow ◽  
Linear Instability ◽  
Base Flow ◽  
Nonlinear Regime ◽  
Weakly Nonlinear ◽  
Corrugated Tube

Abstract Both linear and weakly nonlinear stability of a core annular flow in a corrugated tube in the limit of thin film and small corrugation are examined. Asymptotic techniques are used to derive the corrugated base flow and corresponding linear and weakly nonlinear stability equations. Interesting features show that the corrugation interaction can excite linear instability, but the nonlinearity still can suppress such instability in the weakly nonlinear regime.

Hydromagnetic Stability of a Thin Viscoelastic Magnetic Fluid on Coating Flow Using Landau Equation

2016 ◽  
Vol 32 (5) ◽  
pp. 643-651 ◽  
Author(s):  
C.-K. Chen ◽  
M.-C. Lin
Keyword(s):  
Viscoelastic Fluid ◽  
Nonlinear Stability ◽  
Film Flow ◽  
Landau Equation ◽  
Ginzburg Landau ◽  
Viscoelastic Parameter ◽  
Weakly Nonlinear ◽  
Linear Mode ◽  
Coating Flow ◽  
The One

AbstractThis paper investigates the weakly nonlinear stability of a thin axisymmetric viscoelastic fluid with hydromagnetic effects on coating flow. The governing equation is resolved using long-wave perturbation method as part of an initial value problem for spatial periodic surface waves with the Walter's liquid B type fluid. The most unstable linear mode of a film flow is determined by Ginzburg-Landau equation (GLE). The coefficients of the GLE are calculated numerically from the solution of the corresponding stability problem on coating flow. The effect of a viscoelastic fluid under an applied magnetic field on the nonlinear stability mechanism is studied in terms of the rotation number, Ro, viscoelastic parameter, k, and the Hartmann constant, m. Modeling results indicate that the Ro, k and m parameters strongly affect the film flow. Enhancing the magnetic effects is found to stabilize the film flow when the viscoelastic parameter destabilizes the one in a thin viscoelastic fluid.

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