Plane-parallel advective flow in a horizontal incompressible fluid layer with rigid boundaries

2014 ◽  
Vol 49 (4) ◽  
pp. 438-442 ◽  
Author(s):  
E. G. Schwarz
Keyword(s):  
Incompressible Fluid ◽  
Fluid Layer ◽  
Advective Flow ◽  
Plane Parallel

scholarly journals Gravitational and Dynamical Instabilities of a Decelerating Plane-Parallel Slab of Finite Thickness

1988 ◽  
Vol 101 ◽  
pp. 509-512
Author(s):  
G. Mark Voit
Keyword(s):  
Star Formation ◽  
Interstellar Medium ◽  
Incompressible Fluid ◽  
Gravity Wave ◽  
Finite Thickness ◽  
Blast Waves ◽  
Plane Parallel ◽  
The Stability ◽  
Dynamical Instabilities ◽  
Symmetric And Antisymmetric Modes

AbstractIn order to explore how supernova blast waves might catalyze star formation, we investigate the stability of a slab of decelerating gas of finite thickness. We examine the early work in the field by Elmegreen and Lada and Elmegreen and Elmegreen and demonstrate that it is flawed. Contrary to their claims, blast waves can indeed accelerate the rate of star formation in the interstellar medium. Also, we demonstrate that in an incompressible fluid, the symmetric and antisymmetric modes in the case of zero acceleration transform continuously into Rayleigh-Taylor and gravity-wave modes as acceleration grows more important.

Transition in Homogeneously Heated Inclined Plane Parallel Shear Flows

2003 ◽  
Vol 125 (5) ◽  
pp. 795-803 ◽  
Author(s):  
S. Generalis ◽  
M. Nagata
Keyword(s):  
Shear Flows ◽  
Numerical Study ◽  
Fluid Layer ◽  
Travelling Wave ◽  
Inclined Plane ◽  
Vertical Orientation ◽  
Plane Parallel ◽  
Wide Range ◽  
Parallel Shear Flows ◽  
Roll Type

The transition of internally heated inclined plane parallel shear flows is examined numerically for the case of finite values of the Prandtl number Pr. We show that as the strength of the homogeneously distributed heat source is increased the basic flow loses stability to two-dimensional perturbations of the transverse roll type in a Hopf bifurcation for the vertical orientation of the fluid layer, whereas perturbations of the longitudinal roll type are most dangerous for a wide range of the value of the angle of inclination. In the case of the horizontal inclination transverse roll and longitudinal roll perturbations share the responsibility for the prime instability. Following the linear stability analysis for the general inclination of the fluid layer our attention is focused on a numerical study of the finite amplitude secondary travelling-wave solutions (TW) that develop from the perturbations of the transverse roll type for the vertical inclination of the fluid layer. The stability of the secondary TW against three-dimensional perturbations is also examined and our study shows that for Pr=0.71 the secondary instability sets in as a quasi-periodic mode, while for Pr=7 it is phase-locked to the secondary TW. The present study complements and extends the recent study by Nagata and Generalis (2002) in the case of vertical inclination for Pr=0.

Stability of Two-Immiscible-Fluid Systems: A Review of Canonical Plane Parallel Flows

2016 ◽  
Vol 138 (10) ◽  
Author(s):  
Alireza Mohammadi ◽  
Alexander J. Smits
Keyword(s):  
Fluid Layer ◽  
Future Research ◽  
Immiscible Fluid ◽  
Weakly Nonlinear ◽  
Plane Parallel ◽  
Fluid Systems ◽  
Parallel Flows ◽  
Lower Fluid ◽  
And Performance ◽  
The Stability

A brief review is given on the stability of two-fluid systems. Our interest is primarily driven by drag reduction using superhydrophobic surfaces (SHS) or liquid-infused surfaces (LIS) where the longevity and performance strongly depends on the flow stability. Although the review is limited to immiscible, incompressible, Newtonian fluids with constant properties, the subject is rich in complexity. We focus on three canonical plane parallel flows as part of the general problem: pressure-driven flow, shear-driven flow, and flow down an inclined plane. Based on the linear stability, the flow may become unstable to three modes of instabilities: a Tollmein–Schlichting wave in either the upper fluid layer or the lower fluid layer, and an interfacial mode. These instabilities may be further categorized according to the physical mechanisms that drive them. Particular aspects of weakly nonlinear analyses are also discussed, and some directions for future research are suggested.

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