Stability of Gortler Vortices in Boundary Layers

Floryan, J. M.; Saric, William S.

doi:10.2514/3.51076

Cited by 181 publications

(92 citation statements)

References 17 publications

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“…The mean counter rotating vortex flow that subsequently develops is long and slender in the streamwise extent with strong streamwise velocity and relatively weak cross-sectional velocities, thus leading to the parabolized Laplacian in the cross-sectional yz -plane,V 2 yz . The curvature effects appear only in the y-momentum equation (Floryan & Saric 1982;Hall 1983) as envisioned in the parallel flow formulation of Götler (1940). By choice, the mean flow is here renormalized by the same scale as for the fluctuation equations to follow for convenience in the joint calculation of flow development downstream.…”

Section: (B ) Formulation Of the Heat Transport Problemmentioning

confidence: 99%

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Nonlinear instability of developing streamwise vortices with applications to boundary layer heat transfer intensification through an extended Reynolds analogy

Liu

2008

Phil. Trans. R. Soc. A.

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The intent of the present contribution is to explain theoretically the experimentally measured surface heat transfer rates on a slightly concave surface with a thin boundary layer in an otherwise laminar flow. As the flow develops downstream, the measured heat transfer rate deviates from the local laminar value and eventually exceeds the local turbulent value in a non-trivial manner even in the absence of turbulence. While the theory for steady strong nonlinear development of streamwise vortices can bridge the heat transfer from laminar to the local turbulent value, further intensification is attributable to the transport effects of instability of the basic steady streamwise vortex system. The problem of heat transport by steady and fluctuating nonlinear secondary instability is formulated. An extended Reynolds analogy for Prandtl number unity, PrZ1, is developed, showing the similarity between streamwise velocity and the temperature. The role played by the fluctuation-induced heat flux is similar to momentum flux by the Reynolds shear stress. Inferences from the momentum problem indicate that the intensified heat flux developing well beyond the local turbulent value is attributed to the transport effects of the nonlinear secondary instability, which leads to the formation of 'coherent structures' of the flow. The basic underlying pinions of the non-linear hydrodynamic stability problem are the analyses of J. T. Stuart, which uncovered physical mechanisms of nonlinearities that are crucial to the present developing boundary layers supporting streamwise vortices and their efficient scalar transporting mechanisms.

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Section: (B ) Formulation Of the Heat Transport Problemmentioning

confidence: 99%

“…The basic steady streamwise vortex flow was recognized by Floryan & Saric (1982) and Hall (1983Hall ( , 1988 to be an upstream initial-value problem, which is parabolic in nature. This is in contrast to the linear eigenvalue problem posed originally by Görtler (1940).…”

Section: Heat Transport Via Advection By Nonlinear Instability Of Strmentioning

confidence: 99%

Nonlinear instability of developing streamwise vortices with applications to boundary layer heat transfer intensification through an extended Reynolds analogy

Liu

2008

Phil. Trans. R. Soc. A.

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“…Some measurements have been gathered in atmospheric boundary layers [e.g., Klewicki et al, 1995], but interactions with sediment transport processes have not been established. Such vortices are usually associated with flow over curved surfaces in the form of Taylor-Görtler vortices [Floryan and Saric, 1982] or may be associated with the curvature of individual eddies and hairpin vortices shed by burst sweep events [Blackwelder, 1983;Myose and Blackwelder, 1991]. The vortices bring high-speed fluid close to the bed, which could initiate or increase local saltation rates and may further guide the saltation layer into streamwise concentrations of moving sand.…”

Section: Bed Surface Controlmentioning

confidence: 99%

Formation and behavior of aeolian streamers

2005

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[1] Field experiments were conducted to determine the characteristic spatial and temporal dimensions and behavior of aeolian streamers and to identify the processes responsible for their formation. An instrument array that included anemometer towers, piëzo-electric transport sensors (Safires), and hot-film probes was deployed to measure streamers and airflow dynamics on both a coastal dune and a desert sand mound in California. Aeolian transport occurs predominantly in the form of families of intertwining and bifurcating streamers, while under intense wind forcing, more complex patterns of nested streamers and clouds with embedded streamers develop. The streamers display a characteristic width of approximately 0.2 m and an average lateral spacing of about 1 m. These dimensions appear to be independent of mean airflow characteristics. The observations and measurements of streamers under different environmental conditions suggest that bed surface control in the form of differentiation in moisture content, grain size, or microtopography is not a necessary condition for the formation of streamers. The results show little correlation between possible streamwise vortices or burst sweep events and streamers. It is proposed that streamers are generated by near-surface gusts that originate from large eddies propagating to the ground from higher regions of the boundary layer. These elongated and stretched eddies scrape across the surface and initiate saltation along their path. This concept accounts for the characteristic size and spacing of streamers, their rapid propagation, and the fast response of saltation to wind speed fluctuations.

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“…Görtler vortices at their onset are very weak (Floryan [8], Peerhossaini and Wesferid [9]). According to the linear theory, the boundary layer becomes unstable at some critical Görtler number (for instance, at θ G = 0.46 in Floryan and Saric [10]), and its linear amplification (half of its growth in terms of axial distance) occurs before any disturbance can be detected. • zone OA: this zone corresponds to the leading edge and its junction with the concave part.…”

Section: Effects Of Görtler Instability On the Wall Heat Transfermentioning

confidence: 99%