Linear Stability Analysis of Pulsatile Quasi-Two-Dimensional Duct Flows under a Transverse Magnetic Field

This paper starts with a generalized Burton, Cabrera and Frank (BCF) model by considering the energetic contribution of the adjacent terraces to the step chemical potential. We use the linear stability analysis of the quasistatic free-boundary problem for a two-dimensional step separated by broad terraces to study the step-meandering instabilities. The results show that the equilibrium adatom coverage has influence on the morphological instabilities.

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Similarity solutions for two-dimensional magnetogasdynamic boundary layer flow in a transverse magnetic field

Il Nuovo Cimento D ◽

10.1007/bf02451088 ◽

1986 ◽

Vol 8 (6) ◽

pp. 635-646

Author(s):

J. L. Bansal ◽

R. N. Jat

Keyword(s):

Magnetic Field ◽

Boundary Layer ◽

Transverse Magnetic Field ◽

Boundary Layer Flow ◽

Transverse Magnetic ◽

Similarity Solutions ◽

Two Dimensional ◽

Layer Flow

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Linear stability of confined flow around a 180-degree sharp bend

Journal of Fluid Mechanics ◽

10.1017/jfm.2017.266 ◽

2017 ◽

Vol 822 ◽

pp. 813-847 ◽

Cited By ~ 4

Author(s):

Azan M. Sapardi ◽

Wisam K. Hussam ◽

Alban Pothérat ◽

Gregory J. Sheard

Keyword(s):

Reynolds Number ◽

Stability Analysis ◽

Linear Stability ◽

Linear Stability Analysis ◽

Critical Reynolds Number ◽

Three Dimensional ◽

Base Flow ◽

Two Dimensional ◽

Two Dimensional Flow ◽

The Stability

This study seeks to characterise the breakdown of the steady two-dimensional solution in the flow around a 180-degree sharp bend to infinitesimal three-dimensional disturbances using a linear stability analysis. The stability analysis predicts that three-dimensional transition is via a synchronous instability of the steady flows. A highly accurate global linear stability analysis of the flow was conducted with Reynolds number $\mathit{Re}<1150$ and bend opening ratio (ratio of bend width to inlet height) $0.2\leqslant \unicode[STIX]{x1D6FD}\leqslant 5$. This range of $\mathit{Re}$ and $\unicode[STIX]{x1D6FD}$ captures both steady-state two-dimensional flow solutions and the inception of unsteady two-dimensional flow. For $0.2\leqslant \unicode[STIX]{x1D6FD}\leqslant 1$, the two-dimensional base flow transitions from steady to unsteady at higher Reynolds number as $\unicode[STIX]{x1D6FD}$ increases. The stability analysis shows that at the onset of instability, the base flow becomes three-dimensionally unstable in two different modes, namely a spanwise oscillating mode for $\unicode[STIX]{x1D6FD}=0.2$ and a spanwise synchronous mode for $\unicode[STIX]{x1D6FD}\geqslant 0.3$. The critical Reynolds number and the spanwise wavelength of perturbations increase as $\unicode[STIX]{x1D6FD}$ increases. For $1<\unicode[STIX]{x1D6FD}\leqslant 2$ both the critical Reynolds number for onset of unsteadiness and the spanwise wavelength decrease as $\unicode[STIX]{x1D6FD}$ increases. Finally, for $2<\unicode[STIX]{x1D6FD}\leqslant 5$, the critical Reynolds number and spanwise wavelength remain almost constant. The linear stability analysis also shows that the base flow becomes unstable to different three-dimensional modes depending on the opening ratio. The modes are found to be localised near the reattachment point of the first recirculation bubble.

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