A Property of the energy stability limit for plane parallel shear flow

1972 ◽  
Vol 47 (1) ◽  
pp. 28-35 ◽  
Author(s):  
F. H. Busse
Keyword(s):  
Shear Flow ◽  
Stability Limit ◽  
Energy Stability ◽  
Plane Parallel ◽  
Parallel Shear Flow

On the Stability of Plane Parallel Flow Between Differentially Heated, Tilted Planes

1974 ◽  
Vol 41 (3) ◽  
pp. 554-556 ◽  
Author(s):  
P. S. Ayyaswamy
Keyword(s):  
Stability Limit ◽  
Parallel Flow ◽  
Energy Stability ◽  
Interesting Application ◽  
Plane Parallel ◽  
The Stability

The linear and energy theories of stability of a plane parallel, antisymmetric flow between differentially heated, tilted planes are examined. The linear and energy results do not coincide indicating that subcritical motion may be possible. Also, it is seen that the energy stability limit corresponds to solutions independent of the coordinate in the direction of the flow. An interesting application of Busse’s theorem in this context is demonstrated.

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.

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