Streamwise vortices in shear flows: harbingers of transition and the skeleton of coherent structures

2010 ◽  
Vol 661 ◽  
pp. 178-205 ◽  
Author(s):  
PHILIP HALL ◽  
SPENCER SHERWIN
Keyword(s):  
Coherent Structures ◽  
Shear Flows ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Wave Interaction ◽  
Streamwise Vortex ◽  
Navier Stokes ◽  
Turbulent Shear ◽  
Turbulent Shear Flows ◽  
External Flows

The relationship between asymptotic descriptions of vortex–wave interactions and more recent work on ‘exact coherent structures’ is investigated. In recent years immense interest has been focused on so-called self-sustained processes in turbulent shear flows where the importance of waves interacting with streamwise vortex flows has been elucidated in a number of papers. In this paper, it is shown that the so-called ‘lower branch’ state which has been shown to play a crucial role in these self-sustained processes is a finite Reynolds number analogue of a Rayleigh vortex–wave interaction with scales appropriately modified from those for external flows to Couette flow, the flow of interest here. Remarkable agreement between the asymptotic theory and numerical solutions of the Navier–Stokes equations is found even down to relatively small Reynolds numbers, thereby suggesting the possible importance of vortex–wave interaction theory in turbulent shear flows. The relevance of the work to more general shear flows is also discussed.

Coherent Structures in Turbulent Shear Flows

1990 ◽  
Vol 43 (5S) ◽  
pp. S203-S209 ◽  
Author(s):  
J. M. Wallace ◽  
F. Hussain
Keyword(s):  
Coherent Structures ◽  
Shear Flows ◽  
Turbulent Shear ◽  
Turbulent Shear Flows ◽  
Kinematic Properties

What is firmly known about the kinematic properties and dynamic importance of coherent structures in bounded and unbounded turbulent shear flows is briefly summarized. The nature of instabilities giving rise to these structures is discussed. Unanswered questions requiring further research are posed.

On the instability of vortex–wave interaction states

2016 ◽  
Vol 802 ◽  
pp. 634-666 ◽  
Author(s):  
Kengo Deguchi ◽  
Philip Hall
Keyword(s):  
Reynolds Number ◽  
Coherent Structures ◽  
Time Scale ◽  
Stokes Equations ◽  
Wave Interaction ◽  
Navier Stokes ◽  
Edge States ◽  
Asymptotic Approach ◽  
Navier Stokes Equations ◽  
High Reynolds

In recent years it has been established that vortex–wave interaction theory forms an asymptotic framework to describe high Reynolds number coherent structures in shear flows. Comparisons between the asymptotic approach and finite Reynolds number computations of equilibrium states from the full Navier–Stokes equations have suggested that the asymptotic approach is extremely accurate even at quite low Reynolds numbers. However, unlike the situation with an approach based on solving the full Navier–Stokes equations numerically, the vortex–wave interaction approach has not yet been developed to study the instability of the structures it describes. In this work, a comprehensive study of the different instabilities of vortex–wave interaction states is given and it is shown that there are three different time scales on which instabilities can develop. The most dangerous type is a rapidly growing Rayleigh instability of the streak part of the flow. The least dangerous type is a slow mode operating on the diffusion time scale of the roll–streak part of the flow. The third mode of instability, which we will refer to as the edge mode of instability, occurs on a time scale midway between those of the other two modes. The existence of the latter mode explains why some exact coherent structures can act as edge states between the laminar and turbulent attractors. These stability results are compared to results from Navier–Stokes calculations.

Pattern-recognized structures in bounded turbulent shear flows

1977 ◽  
Vol 83 (4) ◽  
pp. 673-693 ◽  
Author(s):  
James M. Wallace ◽  
Robert S. Brodkey ◽  
Helmut Eckelmann
Keyword(s):  
Reynolds Stress ◽  
Coherent Structures ◽  
Shear Flows ◽  
Local Maximum ◽  
Total Sample ◽  
Turbulent Shear ◽  
Turbulence Structures ◽  
Signal Pattern ◽  
Turbulent Shear Flows ◽  
High Reynolds

It is now well established that coherent structures exist in turbulent shear flows. It should be possible to recognize these in the turbulence signals and to program a computer to extract and ensemble average the corresponding portions of the signals in order to obtain the characteristics of the structures. In this work only the u-signal patterns are recognized, using several simple criteria; simultaneously, however, the v or w signals as well as uv or uw are also processed. It is found that simple signal shapes describe the turbulence structures on the average. The u-signal pattern consists of a gradual deceleration from a local maximum followed by a strong acceleration. This pattern is found in over 65% of the total sample in the region of high Reynolds-stress production. The v signal is found to be approximately 180° out of phase with the u signal. These signal shapes can be easily associated with the coherent structures that have been observed visually. Their details have been enhanced by quadrant truncating. These results are compared with randomly generated signals processed by the same method.

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