Bounds on the energy stability limit of plane parallel shear flows

2001 ◽  
Vol 52 (4) ◽  
pp. 573-596 ◽  
Author(s):  
R. Kaiser ◽  
B. J. Schmitt
Keyword(s):  
Shear Flows ◽  
Stability Limit ◽  
Energy Stability ◽  
Plane Parallel ◽  
Parallel Shear Flows

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.

Transition in plane parallel shear flows heated internally

2004 ◽  
Vol 332 (1) ◽  
pp. 9-16 ◽  
Author(s):  
Masato Nagata ◽  
Sotos Generalis
Keyword(s):  
Shear Flows ◽  
Plane Parallel ◽  
Parallel Shear Flows

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.

scholarly journals On the role of vortex stretching in energy optimal growth of three-dimensional perturbations on plane parallel shear flows

2012 ◽  
Vol 707 ◽  
pp. 369-380 ◽  
Author(s):  
H. Vitoshkin ◽  
E. Heifetz ◽  
A. Yu. Gelfgat ◽  
N. Harnik
Keyword(s):  
Shear Flows ◽  
Plane Waves ◽  
Three Dimensional ◽  
Energy Growth ◽  
Plane Parallel ◽  
Optimal Energy ◽  
Parallel Shear Flows ◽  
Spanwise Vorticity ◽  
Background Shear

AbstractThe three-dimensional linearized optimal energy growth mechanism, in plane parallel shear flows, is re-examined in terms of the role of vortex stretching and the interplay between the spanwise vorticity and the planar divergent components. For high Reynolds numbers the structure of the optimal perturbations in Couette, Poiseuille and mixing-layer shear profiles is robust and resembles localized plane waves in regions where the background shear is large. The waves are tilted with the shear when the spanwise vorticity and the planar divergence fields are in (out of) phase when the background shear is positive (negative). A minimal model is derived to explain how this configuration enables simultaneous growth of the two fields, and how this mutual amplification affects the optimal energy growth. This perspective provides an understanding of the three-dimensional growth solely from the two-dimensional dynamics on the shear plane.

scholarly journals Exact coherent structures in an asymptotically reduced description of parallel shear flows

2014 ◽  
Vol 47 (1) ◽  
pp. 015504 ◽  
Author(s):  
Cédric Beaume ◽  
Edgar Knobloch ◽  
Gregory P Chini ◽  
Keith Julien
Keyword(s):  
Coherent Structures ◽  
Shear Flows ◽  
Parallel Shear Flows
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