On free oscillations of a viscous incompressible fluid in semi-infinite channel

Bogdanova, E. V.; Ryzhov, O. S.

doi:10.1016/0021-8928(83)90032-1

Cited by 2 publications

(8 citation statements)

References 8 publications

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“…The boundary layer emanating from the leading edge of the pipe wall 'fills' the pipe only very far from the inlet. So at high Reynolds numbers there is a vast region of developing flow, the instability of which will be considered here following Smith & Bodonyi (1980), Bogdanova & Ryzhov (1983) and Bogdanova (1982).…”

Section: Problem Formulationmentioning

confidence: 99%

“…In the lower deck, which is of primary concern in the triple-deck theory, we put (Smith 1976;Smith & Bodonyi 1980;Bogdanova 1982)…”

Section: Problem Formulationmentioning

confidence: 99%

“…This pressure is produced by means of the interaction of the lower deck with the outer region of an inviscid irrotational flow. The flow in the outer region turns out to be governed by the Prandtl-Glauert equation, solution of which may be symbolically written as where the linear operator 2 is defined by its spectrum A (see, for example, Smith 1976;Bogdanova 1982) :…”

Section: ( U V W P ) = ( a U -A 3 V A W A~pmentioning

confidence: 99%

“…Further formulation of the problem depends on the relation between A and R-i. Bodonyi 1980and later by Bogdanova (1982) and Bogdanova & Ryzhov (1983). They investigated small free flow oscillations of the kind (3.1) with no-slip ensured at the wall…”

Section: U -Y + a mentioning

confidence: 99%

“…Smith (1976) first applied triple-deck theory to stationary problems of inlet flows (in pipes and channels). Instability problems of entry flows then were studied by Smith & Bodonyi (1980), Bogdanova (1982) and Bogdanova & Ryzhov (1983). However, these studies were restricted to the analysis of normal modes with particular attention to linear neutral waves.…”

Section: Introductionmentioning

confidence: 99%

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Wave packets, resonant interactions and soliton formation in inlet pipe flow

Savenkov¹

1993

J. Fluid Mech.

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The development of disturbances (two-dimensional non-linear and three-dimensional linear) in the entrance region of a circular pipe is studied in the limit of Reynolds number R → ∞ in the framework of triple-deck theory. It is found that lower-branch axisymmetric disturbances can interact in the resonant manner. Numerical calculations show that a two-dimensional nonlinear wave packet grows much more rapidly than that in the boundary layer on a flat plate, producing a spike-like solution which seems to become singular at a finite time. Large-sized, short-scaled disturbances are also studied. In this case the development of axisymmetric disturbances is governed by single one-dimensional equation in the form of the Korteweg-de Vries and Benjamin-Ono equations in the long- and short-wave limits respectively. The nonlinear interactions of these disturbances lead to the formation of solitons which can run both upstream and downstream. Linear three-dimensional wave packets are also calculated.

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Section: Problem Formulationmentioning

confidence: 99%

“…In the lower deck, which is of primary concern in the triple-deck theory, we put (Smith 1976;Smith & Bodonyi 1980;Bogdanova 1982)…”

Section: Problem Formulationmentioning

confidence: 99%

Section: ( U V W P ) = ( a U -A 3 V A W A~pmentioning

confidence: 99%

Section: U -Y + a mentioning

confidence: 99%