The secondary instability in Goertler flow

Yu, Xiaoqiang; Liu, J. T. C.

doi:10.1063/1.857913

Cited by 62 publications

(74 citation statements)

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“…The high inflectional shear layer is provided by vu/vy in the upwash (nO0) region in the centre of the mushroom and, as we now know, predominantly supports the varicose mode of secondary instability (Sabry et al 1990;Yu & Liu 1991;Souza et al 2004); this is discussed and shown earlier by Stuart (1965) as a region supporting intense oscillations. The normal-to-wall mean vorticity, vu/vz, provides strong inflectional shear layers when viewed in the normal-to-wall direction in the likes of a jet or a wake profile and this partially supports the sinuous mode (Sabry et al 1990;Yu & Liu 1991). In terms of energy conversion from the mean flow to the fluctuations, there are now the dual mechanisms The fluctuation temperature is simply a passive scalar, with scales imposed by the advection velocities.…”

Section: Discussion Of Physical Mechanisms Of Developing Nonlinear Sementioning

confidence: 89%

“…The first is the familiar normal-to-wall advection of the spanwise vorticity in parallel or nearly parallel shear flows (Stuart 1956a(Stuart ,b, 1958, which tends to reinforce travelling waves of an opportune phase relation as explained by Lin (1955); the second is the spanwise advection of normal-to-wall vorticity similar to the instability of a three-dimensional steady vortex flow (Sabry et al 1990;Yu & Liu 1991, 1994. The three-dimensional nature of the streamwise velocity can be visualized locally as a two-dimensional one in the cross-sectional yz -plane bounded by the mushroom-like structure (e.g.…”

Section: Discussion Of Physical Mechanisms Of Developing Nonlinear Sementioning

confidence: 99%

“…The centrifugal force exerts its influence on the large-scale mean flow, but does not affect the short-scale secondary instability to leading order (Hall & Horseman 1991;Yu & Liu 1991).…”

Section: (B ) Formulation Of the Heat Transport Problemmentioning

confidence: 99%

“…denotes the complex conjugate;qðx; y; zÞ represents the complex amplitude or wave envelopû;v;ŵ;q for the fluctuations; the streamwise secondary instability wavenumber is a; and the frequency is u. The wavy characteristics are assumed to be fixed by the imposed upstream initial value according to Yu & Liu (1991) and according to experiments. The mean steady flow has spanwise wavelength of l z .…”

Section: Outline Of the Calculation Scheme For The Nonlinear Momentummentioning

confidence: 99%

“…The computation begins by assigning initial amplitude for the secondary instability with shape functions from Yu & Liu (1991) and with a, u and l z fixed throughout the flow as already discussed. The Reynolds stresses are then calculated and used to modify the mean field to advance one Dx step.…”

Section: Outline Of the Calculation Scheme For The Nonlinear Momentummentioning

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: Discussion Of Physical Mechanisms Of Developing Nonlinear Sementioning

confidence: 89%

Section: Discussion Of Physical Mechanisms Of Developing Nonlinear Sementioning

confidence: 99%

“…The centrifugal force exerts its influence on the large-scale mean flow, but does not affect the short-scale secondary instability to leading order (Hall & Horseman 1991;Yu & Liu 1991).…”

Section: (B ) Formulation Of the Heat Transport Problemmentioning

confidence: 99%

Section: Outline Of the Calculation Scheme For The Nonlinear Momentummentioning

confidence: 99%

Section: Outline Of the Calculation Scheme For The Nonlinear Momentummentioning

confidence: 99%

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