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CALCULATION OF THE LINEAR STABILITY OF LIQUID FLOW IN A FLAT CHANNEL WITH STREAMWISE WAVY WALLS

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Abstract

The full Navier–Stokes equations are used to study the linear stability of plane Poiseuille flow in a channel with the lower wall corrugated along the flow, due to which the flow has two velocity components. A generalized eigenvalue problem is solved numerically. Three types of perturbations are considered: plane periodic (zero Floquet parameter), plane doubly periodic (finite values of the Floquet parameter), and spatial perturbations. Neutral curves are analyzed in a wide range of the corrugation parameter and Reynolds number. It is found that the critical Reynolds number above which time-growing perturbations appear depends in a complex way on the dimensionless amplitude and period of corrugation. It is shown that in the case of flow in a channel with corrugated wall, three-dimensional perturbations are usually more dangerous. The exception is the small amplitude of corrugation at which plane perturbations are more dangerous.

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  1. Institute of Thermophysics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, Russia

    Yu. Ya. Trifonov

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Correspondence to Yu. Ya. Trifonov.

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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, 2023, Vol. 64, No. 6, pp. 68-80. https://doi.org/10.15372/PMTF20230609.

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Trifonov, Y.Y. CALCULATION OF THE LINEAR STABILITY OF LIQUID FLOW IN A FLAT CHANNEL WITH STREAMWISE WAVY WALLS. J Appl Mech Tech Phy 64, 1000–1010 (2023). https://doi.org/10.1134/S0021894423060093

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  • DOI: https://doi.org/10.1134/S0021894423060093

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