Instability of plane parallel shear flow (toward a mechanistic picture of how it works)

1988 ◽  
Vol 126 (1) ◽  
pp. 103-121 ◽  
Author(s):  
Richard S. Lindzen
Keyword(s):  
Shear Flow ◽  
Plane Parallel ◽  
Parallel Shear Flow

The viscous secondary flow ahead of an infinite cylinder in a uniform parallel shear flow

1960 ◽  
Vol 7 (1) ◽  
pp. 145-155 ◽  
Author(s):  
Alar Toomre
Keyword(s):  
Shear Flow ◽  
Lateral Displacement ◽  
Reynolds Numbers ◽  
Infinite Cylinder ◽  
List Type ◽  
Displacement Effect ◽  
Simple Method ◽  
Viscous Shear ◽  
Parallel Shear Flow ◽  
Viscous Shear Flow

A simple method is presented in this paper for calculating the secondary velocities, andthe lateral displacement of total pressure surfaces (i.e. the ‘displacement effect’) in the plane of symmetry ahead of an infinitely long cylinder situated normal to a steady, incompressible, slightly viscous shear flow; the cylinder is also perpendicular to the vorticity, which is assumed uniform but small. The method is based on lateral gradients of pressure, these being calculated from the primary flow alone. Profiles of the secondary velocities are obtained at several Reynolds numbers ahead of two specific cylindrical shapes: a circular cylinder, and a flat plate normal to the flow. The displacement effect is derived and, rathe surprisingly, is found to be virtually independent of the Reynolds number.

On the effect of parallel shear flow on the plasmoid instability

2018 ◽  
Vol 25 (10) ◽  
pp. 102117
Author(s):  
M. Hosseinpour ◽  
Y. Chen ◽  
S. Zenitani
Keyword(s):  
Shear Flow ◽  
Parallel Shear Flow

The extension of the Miles-Howard theorem to compressible fluids

1970 ◽  
Vol 43 (4) ◽  
pp. 833-836 ◽  
Author(s):  
G. Chimonas
Keyword(s):  
Growth Rate ◽  
Shear Flow ◽  
Upper Bound ◽  
Unstable Mode ◽  
Vertical Gradient ◽  
Flow Speed ◽  
Incompressible Fluids ◽  
Compressible Fluids ◽  
Sufficient Condition ◽  
Parallel Shear Flow

A statically stable, gravitationally stratified compressible fluid containing a parallel shear flow is examined for stability against infinitesimal adiabatic perturbations. It is found that the Miles–Howard theorem of incompressible fluids may be generalized to this system, so that n2 ≥ ¼U′2 throughout the flow is a sufficient condition for stability. Here n2 is the Brunt–Väissälä frequency and U’ is the vertical gradient of the flow speed. Howard's upper bound on the growth rate of an unstable mode also generalizes to this compressible system.

Second-order recombination in a parallel shear flow

1989 ◽  
Vol 200 ◽  
pp. 389-407 ◽  
Author(s):  
Ronald Smith
Keyword(s):  
Shear Flow ◽  
Concentration Distribution ◽  
Second Order ◽  
Explicit Solutions ◽  
Far Field ◽  
First Order ◽  
Parallel Shear Flow

For a reactive solute, with weak second-order recombination, an investigation is made of the near-source behaviour (where concentrations are high), and of the far field (where the recombination has an accumulative effect). Despite the loss of material and increased spread due to recombination, the far-field concentration distribution is shown to be nearly Gaussian. This permits a simplified (Gaussian) treatment of the chemical nonlinearity. Explicit solutions are given for the total amount of solute, variance and kurtosis for solutes with no first-order reactions.

The interactive dynamics of flow and directional solidification in a Hele-Shaw cell Part 1. Experimental investigation of parallel shear flow

2002 ◽  
Vol 470 ◽  
pp. 247-268 ◽  
Author(s):  
M. ZHANG ◽  
T. MAXWORTHY
Keyword(s):  
Shear Flow ◽  
Directional Solidification ◽  
Flow Direction ◽  
Velocity Ratio ◽  
Parallel Flow ◽  
Tilting Angle ◽  
Specimen Material ◽  
Parallel Shear Flow ◽  
Crystal Cells ◽  
Hele Shaw Cell

It is recognized that flow in the melt can have a profound influence on the dynamics of a solidifying interface and hence on the quality of the solidified material. To better understand the effect of fluid flow on the interface morphological stability and on the cellular and dendritic growth, directional solidification experiments were carried out in a horizontally placed Hele-Shaw cell with and without externally imposed parallel shear flow. The specimen material used was SCN–1.0 Wt% acetone. The experiment shows that the transient parallel flow has a stabilizing effect on the planar interface by damping the existing initial perturbations. The left–right symmetry of crystal cells was broken by the parallel flow, with cells tilting toward the incoming flow direction. The tilting angle increased with the velocity ratio. The secondary dendrites were found to either not appear or appear much later on the downstream side of the crystal cells. The wavelengths of the initial perturbations and of the cellular interface were insensitive to the imposed flow.

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