{"title":"紊流边界层的位移-厚度、壁层和中流尺度,以及通道和管道流动的涡量段塞","authors":"F. Smith, D. Doorly, A. Rothmayer","doi":"10.1098/rspa.1990.0034","DOIUrl":null,"url":null,"abstract":"This theoretical study is motivated by the experimental observations (a) on the thickening of a turbulent boundary layer compared with its laminar counterpart, (b) on the erupting tongue of fluid that forms the leading edge of a turbulent spot in a boundary layer, (c) on the wall-layer and mid-flow scales, and (d) on the slugs of vorticity that occur in the middle of turbulent channel and pipe flows. It appears that no previous rational explanation has been put forward for these experimental observations. The present tentative suggestions for (a), (b) and (d) centre on the existence of small-deficit fast-travelling zones of concentrated vorticity governed by the nonlinear Euler equations to leading order at high Reynolds numbers Re but crucially influenced by viscosity nevertheless. In the boundary-layer case these zones travel outside the original boundary layer and hence act to increase the effective boundary-layer thickness. The structure of such zones and their scales, governing equations and amplitude dependence are discussed for assumed planar boundary layers and channel flows and for three-dimensional pipe flows in turn. Allied with this, the theory addresses the closure of the amplitude-dependent neutral curve at high Reynolds numbers, the connection with other Euler-type flows and the possibility of delay in sublayer bursting, as well as aiming to give some guidance on nonlinear aspects of unsteady two- and three-dimensional computations for Euler and related flows. The aspects in (c) above, concerning the turbulent scales both of the thin wall layer (O(Re-1 In Re), from a renormalizing and scale-cascade argument) and of the thicker mid-flow zone (containing the Kolmogorov microscale O(Re-3/4)) which lies between that layer and the extensive small-deficit outer zone, are also discussed tentatively in terms of their dynamics, leading to apparently good agreement with turbulent-flow experiments and empirical models, for those scales. Other qualitative comparisons are presented.","PeriodicalId":20605,"journal":{"name":"Proceedings of the Royal Society of London. A. 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It appears that no previous rational explanation has been put forward for these experimental observations. The present tentative suggestions for (a), (b) and (d) centre on the existence of small-deficit fast-travelling zones of concentrated vorticity governed by the nonlinear Euler equations to leading order at high Reynolds numbers Re but crucially influenced by viscosity nevertheless. In the boundary-layer case these zones travel outside the original boundary layer and hence act to increase the effective boundary-layer thickness. The structure of such zones and their scales, governing equations and amplitude dependence are discussed for assumed planar boundary layers and channel flows and for three-dimensional pipe flows in turn. Allied with this, the theory addresses the closure of the amplitude-dependent neutral curve at high Reynolds numbers, the connection with other Euler-type flows and the possibility of delay in sublayer bursting, as well as aiming to give some guidance on nonlinear aspects of unsteady two- and three-dimensional computations for Euler and related flows. The aspects in (c) above, concerning the turbulent scales both of the thin wall layer (O(Re-1 In Re), from a renormalizing and scale-cascade argument) and of the thicker mid-flow zone (containing the Kolmogorov microscale O(Re-3/4)) which lies between that layer and the extensive small-deficit outer zone, are also discussed tentatively in terms of their dynamics, leading to apparently good agreement with turbulent-flow experiments and empirical models, for those scales. Other qualitative comparisons are presented.\",\"PeriodicalId\":20605,\"journal\":{\"name\":\"Proceedings of the Royal Society of London. A. 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引用次数: 45
摘要
本理论研究的动机是实验观察(a)湍流边界层与层流边界层相比增厚,(b)形成边界层湍流点前缘的流体喷发舌,(c)壁面层和中流尺度,以及(d)湍流通道和管道流动中间出现的涡量段塞。似乎以前没有人对这些实验观察提出合理的解释。目前对(a)、(b)和(d)的尝试性建议集中在高雷诺数Re下存在由非线性欧拉方程主导的小赤字快行区集中涡度,但仍然受到粘度的重要影响。在边界层的情况下,这些区域在原始边界层之外移动,从而增加了有效边界层厚度。在假定的平面边界层和通道流动以及三维管道流动的情况下,依次讨论了这些区域的结构及其规模、控制方程和振幅依赖性。与此相结合,该理论解决了高雷诺数下振幅相关中性曲线的闭合,与其他欧拉型流动的联系以及亚层破裂延迟的可能性,并旨在对非定常二维和三维欧拉及相关流动计算的非线性方面提供一些指导。上面(c)中关于薄壁层(O(Re-1 in Re),从重整化和尺度级联的角度来看)和位于该层和广泛的小缺陷外区之间的较厚的中流区(包含Kolmogorov微尺度O(Re-3/4))的湍流尺度的各方面,也在其动力学方面进行了初步讨论,导致与这些尺度的湍流实验和经验模型明显吻合。还提出了其他质的比较。
On displacement-thickness, wall-layer and mid-flow scales in turbulent boundary layers, and slugs of vorticity in channel and pipe flows
This theoretical study is motivated by the experimental observations (a) on the thickening of a turbulent boundary layer compared with its laminar counterpart, (b) on the erupting tongue of fluid that forms the leading edge of a turbulent spot in a boundary layer, (c) on the wall-layer and mid-flow scales, and (d) on the slugs of vorticity that occur in the middle of turbulent channel and pipe flows. It appears that no previous rational explanation has been put forward for these experimental observations. The present tentative suggestions for (a), (b) and (d) centre on the existence of small-deficit fast-travelling zones of concentrated vorticity governed by the nonlinear Euler equations to leading order at high Reynolds numbers Re but crucially influenced by viscosity nevertheless. In the boundary-layer case these zones travel outside the original boundary layer and hence act to increase the effective boundary-layer thickness. The structure of such zones and their scales, governing equations and amplitude dependence are discussed for assumed planar boundary layers and channel flows and for three-dimensional pipe flows in turn. Allied with this, the theory addresses the closure of the amplitude-dependent neutral curve at high Reynolds numbers, the connection with other Euler-type flows and the possibility of delay in sublayer bursting, as well as aiming to give some guidance on nonlinear aspects of unsteady two- and three-dimensional computations for Euler and related flows. The aspects in (c) above, concerning the turbulent scales both of the thin wall layer (O(Re-1 In Re), from a renormalizing and scale-cascade argument) and of the thicker mid-flow zone (containing the Kolmogorov microscale O(Re-3/4)) which lies between that layer and the extensive small-deficit outer zone, are also discussed tentatively in terms of their dynamics, leading to apparently good agreement with turbulent-flow experiments and empirical models, for those scales. Other qualitative comparisons are presented.