Stability of the boundary layer above the surface of a wave travelling over a plate

Aizin, L. B.; Volodin, A. G.

doi:10.1007/bf00910544

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Introduction and Problem Formulation1

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1986

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“…Consider a viscous incompressible fluid with a density e and a kinematic viscosity v in a closed domain D with a rigid boundary r; characteristic length of D is equal to d. The governing equations in the dimensionless variables can be written in the following form (3) be an external force. Assume that V = V,(z; R) 7 1., =Po@; R) (4) is a steady solution of the system (1) -(3) at 5 = 0. Assume also that a t R = R, the solution is unstable with respect to the disturbances of the frequency w,, and a t R > R, there is a soft nonlinear development of instability which relax t o a secondary autovibrational regime.…”

Section: Introduction and Problem Formulationmentioning

confidence: 99%

Analysis of an Amplitude Equation for Autovibrational Flow Regimes at Resonance External Forces

Levina¹,

Nepomnyaschiy²

1986

Z Angew Math Mech

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Resonance effects in viscous flows produced by unsteady external forces are studied. With the help of a small parameter method the amplitude equation for a resonance case is derived. It is shown that the amplitude of the secondary regime is proportional to the cubic root amplitude of external force. Possible transitions between supercritical motions are investigated. The map of secondary regimes in dependence on the amplitude equation coefficients is given.

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Section: Introduction and Problem Formulationmentioning

confidence: 99%