On the role of buoyancy in determining the stability of curved mixing layers

Otto, S. R.; Stott, Jillian A. K.; Denier, James P.

doi:10.1063/1.870012

Cited by 3 publications

(4 citation statements)

References 15 publications

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“…These results are reproduced and extended in this paper to show agreement with numerical calculations. Similar modes have been shown to occur within shear layers with a deficit in velocity due to a wake component, Zhuang (1999), and in boundary and mixing layers where a degree of buoyancy is allowed, Stott & Denier (1998) and Otto et al (1999).…”

Section: Introductionsupporting

confidence: 55%

“…Vortices akin to these modes have been studied within the atmosphere, Scorer & Wilson (1963) and Scorer (1997). These structures arise within curved flows occurring due to gravity, Otto, Stott & Denier (1999): they are thought to be a possible mechanism for generating 'clear-air turbulence' within the atmosphere. The analytical part of Otto et al (1996) was concerned with inviscid and viscous right-hand branch modes in a high Taylor/Görtler number régime.…”

Section: Introductionmentioning

confidence: 99%

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Görtler vortices in compressible mixing layers

Sarkies

Otto

2001

J. Fluid Mech.

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In experiments, Plesniak, Mehta & Johnson (1994) have noted that curved two-stream mixing layers are susceptible to centrifugal instabilities under the condition that the slower of the streams curves towards the faster one; this condition is analogous to the concave curvature condition for the stability of the flow over a plate. The modes which arise manifest themselves as vortices aligned with the dominant flow direction. Previous numerical and analytical work has elucidated the structure of these vortices within incompressible mixing layers; Otto, Jackson & Hu (1996). In this paper we go on to investigate the rôles of compressibility and heating in determining the streamwise fate of Görtler vortices within these situations.The development of the disturbances is monitored downstream and curves of neutral stability are plotted. The effect of changing the Mach number and free-stream temperatures is studied in detail. It is found that for certain parameter régimes modes can occur within convexly curved, or ‘stable’ mixing layers; these ‘thermal modes’ have no counterpart within incompressible mixing layers. By making use of a large Görtler number analysis we are able to verify our numerical results, and derive a very simple condition which yields information about the parameter ranges for which certain modes are likely to occur. As an aside this method can be used to show that no degree of wall cooling will allow sustained growth of Görtler vortices within boundary layers over convex plates.

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Section: Introductionsupporting

confidence: 55%

Section: Introductionmentioning

confidence: 99%

Görtler vortices in compressible mixing layers

Sarkies

Otto

2001

J. Fluid Mech.

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“…The two cases of a zero and a non-zero buoyancy parameter will be considered separately. The former case is relatively well understood, or at least when either curvature or buoyancy is present-the boundary layer experiencing the combined effects of curvature and buoyancy has not been studied in depth (with the exception of the inviscid theory of Stott and Denier [23]) but the effects are easily surmised from knowledge of both the individual problems [9,11,14] and the equivalent mixing layer problem [18][19][20]. The buoyancy-coupled boundary layer has received little attention in the literature and thus will be the main focus of attention here.…”

Section: Linear Resultsmentioning

confidence: 99%

“…The effects of the underlying wall curvature are not evident explicitly in the inviscid problem, but are implicit within the basic flow. With no curvature term present in the modified Taylor-Goldstein equation, the analysis of Otto, Stott and Denier [18] cannot be performed and thus stability boundaries may not be derived in the conventional way. It is possible that a consideration of the smaller terms will yield the stability boundaries but this calculation is rather involved and is beyond the scope of this paper.…”

Section: A Note On the Inviscid Stability Boundaries In The Case Of Nmentioning

confidence: 99%

The stability of a curved, heated boundary layer: linear and nonlinear problems

Watson

Otto²

2005

ANZIAM J.

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We consider the stability of high Reynolds number flow past a heated, curved wall. The influence of both buoyancy and curvature, with the appropriate sense, can render a flow unstable to longitudinal vortices. However, conversely each mechanism can make a flow more stable; as with a stable stratification or a convex curvature. This is partially due to their influence on the basic flow and also due to additional terms in the stability equations. In fact the presence of buoyancy in combination with an appropriate local wall gradient can actually increase the wall shear and these effects can lead to supervelocities and the promotion of a wall jet. This leads to the interesting discovery that the flow can be unstable for both concave and convex curvatures. Furthermore, it is possible to observe sustained vortex growth in stably stratified boundary layers over convexly curved walls. The evolution of the modes is considered in both the linear and nonlinear regimes.

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The effects of curvature on wake-dominated incompressible free shear layers

Zhuang

1999

Physics of Fluids

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Instability characteristics of curved incompressible free shear layers, with mean velocity profiles having a wake component, are studied using linear inviscid stability theory in spatial formulation. Both two- and three-dimensional disturbances are considered. The shear layer mode and the wake mode, previously found in a plane shear layer with a wake component in the mean velocity profile, are also found in the corresponding curved shear layer. Results of unstably curved shear layers with a wake component are consistent with those of previous investigations of a curved shear layer without a wake component. Results for a stably curved shear layer with a wake component show that the growth rate of the wake mode increases with increasing shear layer curvature and an oblique wake mode can become dominant compared to its corresponding two-dimensional wake mode. A wake-dominated shear layer, therefore, can become unstable as its curvature increases, regardless of whether the shear layer is stably or unstably curved regarding the corresponding monotonic mixing layer profile. The amplification rates of the shear layer mode and the wake mode could become comparable by varying the free-stream density ratio. For a wake-dominated shear layer under three-dimensional disturbances, the centrifugal modes are found. These modes are developed out of the wake mode for a stably curved shear layer and developed out of the shear layer mode for an unstably curved shear layer. Since the stability behavior is governed by the wake behavior, the wake-dominated shear layer could support the centrifugal instability regardless of the sense of curvature regarding the corresponding monotonic mixing layer profile.

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On the role of buoyancy in determining the stability of curved mixing layers

Cited by 3 publications

References 15 publications

Görtler vortices in compressible mixing layers

Görtler vortices in compressible mixing layers

The stability of a curved, heated boundary layer: linear and nonlinear problems

The effects of curvature on wake-dominated incompressible free shear layers

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