Physics of Transitional Shear Flows

Бойко, А. В.; Dovgal, A. V.; Grek, G. R.; Козлов, В. В.

doi:10.1007/978-94-007-2498-3

Cited by 55 publications

(21 citation statements)

References 93 publications

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“…The simplest one consists in transforming it to a linear problem of larger dimension by forming the so-called companion matrices [20]. A companion matrix for equation (42) …”

Section: ( ))mentioning

confidence: 99%

Study of the Effect of Parietal Suction and Blowing on the Stability of Laminar External Flow

Laouer¹,

Mezaache²,

Laouar³

2016

IJHT

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Stability and transition problems of two dimensional laminar external flow over a flat plate with wall suction and blowing are studied numerically using the temporal linear stability theory. The flow is assumed similar two-dimensional laminar boundary-layer. The mean velocity profiles are obtained numerically for the case of suction or blowing. The stability equation is given in a general form which can be applied to Chebyshev domain and in boundary layer domain and solved numerically by the Chebyshev collocation spectral method. The neutral stability curves and the critical Reynolds numbers are presented.

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“…The simplest one consists in transforming it to a linear problem of larger dimension by forming the so-called companion matrices [20]. A companion matrix for equation (42) …”

Section: ( ))mentioning

confidence: 99%

Study of the Effect of Parietal Suction and Blowing on the Stability of Laminar External Flow

Laouer¹,

Mezaache²,

Laouar³

2016

IJHT

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“…It is thus suggested that a hairpin-regeneration cycle exists at each local scale, until the limiting scales defined by viscous dissipation. This scenario of transition accounts for the preponderance of hairpin structures in transitional boundary layers, as observed in both experiments (Boiko et al 2012) and numerical studies (Wu and Moin 2009).…”

Section: Resultsmentioning

confidence: 52%

A purely nonlinear route to transition approaching the edge of chaos in a boundary layer

et al. 2012

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The understanding of transition in shear flows has recently progressed along new paradigms based on the central role of coherent flow structures and their nonlinear interactions. We follow such paradigms to identify, by means of a nonlinear optimization of the energy growth at short time, the initial perturbation which most easily induces transition in a boundary layer. Moreover, a bisection procedure has been used to identify localized flow structures living on the edge of chaos, found to be populated by hairpin vortices and streaks. Such an edge structure appears to act as a relative attractor for the trajectory of the laminar base state perturbed by the initial finite-amplitude disturbances, mediating the route to turbulence of the flow, via the triggering of a regeneration cycle of and hairpin structures at different space and time scales. These findings introduce a new, purely nonlinear scenario of transition in a boundary-layer flow.

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“…Moreover, if A and E are Hermitian and A is positive or negative definite, then ν = µ, P l = P For example in the interconnect analysis of VLIC [5] and the linear stability analysis of hydrodynamic flows [2]. Without loss of generality we will assume that the matrix A is nonsingular since otherwise the change of variable x =xe ρt , where ρ is chosen such that A − ρE is nonsingular, leads to a system forx of the same form as (4.1) but with a nonsingular matrix A − ρE instead of A.…”

Section: Letmentioning

confidence: 99%

A generalization of matrix inversion with application to linear differential-algebraic systems

Nechepurenko¹,

Sadkane²

2012

ELA

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Abstract. A new generalized inversion for square matrices based on projections is introduced. It includes as special cases known generalized inverses such as the Moore-Penrose and the Drazin inverses. When associated with a regular matrix pencil, it can be expressed by a contour integral formula and can be used, in particular, to write down an explicit representation of the solutions of linear differential algebraic systems. The representation can further be simplified when a well chosen expansion is used for the exponential function. An illustration is given with the expansion in Laguerre functions.

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Physics of Transitional Shear Flows

Cited by 55 publications

References 93 publications

Study of the Effect of Parietal Suction and Blowing on the Stability of Laminar External Flow

Study of the Effect of Parietal Suction and Blowing on the Stability of Laminar External Flow

A purely nonlinear route to transition approaching the edge of chaos in a boundary layer

A generalization of matrix inversion with application to linear differential-algebraic systems

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