Über die Entstehung der Turbulenz

Tollmien, Walter; Schlichting, Hermann; Görtler, Henry; Riegels, F. W.

doi:10.1007/978-3-662-11836-8_66

Cited by 59 publications

(85 citation statements)

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“…Equations (4)- (7) discrete values of v z , v r , v θ , and q. q is eliminated as described in Appendix C1 of [18], as are the boundary values of v z , v r , and v θ using (8) and (9). The result is a (3N − 6) × (3N − 6) standard matrix eigenvalue problem with eigenvalue ω and eigenvector whose elements are the discrete values of v z , v r , and v θ at x = x n for 0 < n < N − 1.…”

Section: Methodsmentioning

confidence: 99%

“…Interested readers should refer to I for more details of the basic flow, including the appearance of a wall jet for S above about 4 and asymptotic analyses of the limits of large rotation rate and large streamwise distance. Stability of the Blasius boundary layer on a flat plate has been extensively studied, the primary instability being due to growth of Tollmien-Schlichting waves (see, for example, [9][10][11]). Stability analysis of a nonrotating cylinder placed in an axial stream was conducted by Tutty [12].…”

Section: Introductionmentioning

confidence: 99%

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Instability of flow around a rotating, semi-infinite cylinder

2016

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Stability of flow around a rotating, semi-infinite cylinder placed in an axial stream is investigated. Assuming large Reynolds number, the basic flow is computed numerically as described by Derebail Muralidhar et al. [Proc. R. Soc. London, Ser. A 472, 20150850 (2016)], while numerical solution of the local stability equations allows calculation of the modal growth rates and hence determination of flow stability or instability. The problem has three nondimensional parameters: the Reynolds number Re, the rotation rate S, and the axial location Z. Small amounts of rotation are found to strongly affect flow stability. This is the result of a nearly neutral mode of the nonrotating cylinder which controls stability at small S. Even small rotation can produce a sufficient perturbation that the mode goes from decaying to growing, with obvious consequences for stability. Without rotation, the flow is stable below a Reynolds number of about 1060 and also beyond a threshold Z. With rotation, no matter how small, instability is no longer constrained by a minimum Re nor a maximum Z. In particular, the critical Reynolds number goes to zero as Z → ∞, so the flow is always unstable at large enough axial distances from the nose. As Z is increased, the flow goes from stability at small Z to instability at large Z. If the critical Reynolds number is a monotonic decreasing function of Z, as it is for S between about 0.0045 and 5, there is a single boundary in Z, which separates the stable from the unstable part of the flow. On the other hand, when the critical Reynolds number is nonmonotonic, there can, depending on the choice of Re, be several such boundaries and flow stability switches more than once as Z is increased. Detailed results showing the critical Reynolds number as a function of Z for different rotation rates are given. We also obtain an asymptotic expansion of the critical Reynolds number at large Z and use perturbation theory to further quantify the behavior at small S.

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Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Instability of flow around a rotating, semi-infinite cylinder

2016

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“…We will consider a Tollmien-Schlichting (TS) [24,25] wave as an example of an unstable flow wave. A TS wave represents a streamwise instability that arises in a viscous boundary layer and also suitably predicts the evolution of a two-dimensional instability in parallel (and nearly parallel) shear flows.…”

Section: (A) Subsurface Dynamical Characteristicsmentioning

confidence: 99%

“…Growing eigensolutions of the Orr-Sommerfeld equation are known as the TS [24,25] waves, which predict the evolution of two-dimensional instabilities in parallel (and nearly parallel) shear flows. TS waves have been observed in laboratory experiments for boundary layers [26,27] and channel flows [28], in which the unstable waves were generated using a vibrating magnetic ribbon.…”

Section: (B) Fluid Model (I) Overviewmentioning

confidence: 99%

Flow stabilization by subsurface phonons

et al. 2015

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The interaction between a fluid and a solid surface in relative motion represents a dynamical process that is central to the problem of laminar-to-turbulent transition (and consequent drag increase) for air, sea and land vehicles, as well as long-range pipelines. This problem may in principle be alleviated via a control stimulus designed to impede the generation and growth of instabilities inherent in the flow. Here, we show that phonon motion underneath a surface may be tuned to passively generate a spatio-temporal elastic deformation profile at the surface that counters these instabilities. We theoretically demonstrate this phenomenon and the underlying mechanism of frequency-dependent destructive interference of the unstable flow waves. The converse process of flow destabilization is illustrated as well. This approach provides a condensed-matter physics treatment to fluid-structure interaction and a new paradigm for flow control.

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“…Tais hipóteses conduzem a uma linearização das equações de Navier-Stokes, que se transformam assim em um problema de valor característico em que as autofunções existem apenas se for satisfeita uma relação de dispersão a partir da qual se pode determinar a estabilidade ou não de perturbações infinitesimais com dados número de onda e frequência. À época da derivação da equação de Orr-Sommerfeld, as teorias assintóticas não estavam suficientemente desenvolvidas para lidar com ela, por isso muito do trabalho subsequente em estabilidade hidrodinâmica consistiu em desenvolver métodos heurísticos de aproximação para soluções desta equação (HEISENBERG, 1924), (TOLLMIEN, 1929), (TOLLMIEN, 1947), (LIN, 1945), (LIN, 1955 MILLER, 1996). A teoria aqui apresentada tem uma extensão para a equação de Ginzburg-Landau (ARANHA, 2004), e suas predições deverão ser confrontadas, futuramente, com aquelas apresentadas nos referidos trabalhos.…”

Section: Estabilidade Hidrodinâmicaunclassified

Escoamento ao redor de um cilindro circular: derivação da equação de Landau a partir das equações de Navier-Stokes.

Lavinas¹

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RESUMOEste trabalho aborda o escoamento incompressível ao redor de um cilindro circular. A tese que se quer defender, com base em experimentos numéricos, é: A equação de Landau pode ser obtida a partir das equações de Navier-Stokes por uma análise de estabilidade não-linear global. A teoria produz um procedimento bem-definido para determinação dos coeficientes da equação de Landau, permitindo assim a sua interpretação como um modelo simplificado (equações reduzidas de Navier-Stokes) para a predição das forças aplicadas pelo fluido ao cilindro, que podem ser comparados com resultados experimentais. O modelo não-linear se baseia em uma teoria assintótica que, como se sabe, tem sua faixa de validade no espaço de parâmetros determinada a posteriori, por meio da própria comparação com dados de laboratório. Resultados na faixa 46 < Re < 80 são apresentados. Descobriu-se, que a faixa de aplicabilidade da teoria como aqui exposta é restrita, não excedendo em muito o valor crítico do número de Reynolds. Argumentos são expostos para justificar esta afirmação e possíveis maneiras de modificar a teoria para estender esta faixa são apresentadas.São reportados, ainda, teoria e resultados sobre um novo tipo de condição de contorno, denominado impedância fluida, que permite reduzir o tamanho do domínio de cálculo necessá-rio para simulação de escoamentos externos, comparativamente à comumente utilizada condição de "outflow". Neste caso, abordou-se a faixa 20 ≤ Re ≤ 600. Theory and results concerning a new type of boundary condition called fluid impedance are also reported, permitting the reduction of the domain size necessary for simulating external flows, comparatively to the commonly used outflow condition. In this case, the range 20 ≤ Re ≤ 600 was considered.

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Über die Entstehung der Turbulenz

Cited by 59 publications

References 0 publications

Instability of flow around a rotating, semi-infinite cylinder

Instability of flow around a rotating, semi-infinite cylinder

Flow stabilization by subsurface phonons

Escoamento ao redor de um cilindro circular: derivação da equação de Landau a partir das equações de Navier-Stokes.

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