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Zh. Vychisl. Mat. Mat. Fiz., 2018, Volume 58, Number 5, Pages 726–740 (Mi zvmmf10733)  

This article is cited in 1 scientific paper (total in 1 paper)

Numerical analysis of spatial hydrodynamic stability of shear flows in ducts of constant cross section

A. V. Boikoab, K. V. Demyankocd, Yu. M. Nechepurenkocd

a Tyumen State University, Tyumen, Russia
b Khristianovich Institute of Theoretical and Applied Mechanics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, Russia
c Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Moscow, Russia
d Institute of Numerical Mathematics, Russian Academy of Sciences, Moscow, Russia

Abstract: A technique for analyzing the spatial stability of viscous incompressible shear flows in ducts of constant cross section, i.e., a technique for the numerical analysis of the stability of such flows with respect to small time-harmonic disturbances propagating downstream is described and justified. According to this technique, the linearized equations for the disturbance amplitudes are approximated in space in the plane of the duct cross section and are reduced to a system of first-order ordinary differential equations in the streamwise variable in a way independent of the approximation method. This system is further reduced to a lower dimension one satisfied only by physically significant solutions of the original system. Most of the computations are based on standard matrix algorithms. This technique makes it possible to efficiently compute various characteristics of spatial stability, including finding optimal disturbances that play a crucial role in the subcritical laminar-turbulent transition scenario. The performance of the technique is illustrated as applied to the Poiseuille flow in a duct of square cross section.

Key words: duct flows, spatial stability, spectral reduction, optimal disturbances.

Funding Agency Grant Number
Russian Foundation for Basic Research 16-08-00354_а
16-31-60092_мол_а_дк
Russian Academy of Sciences - Federal Agency for Scientific Organizations


DOI: https://doi.org/10.7868/S0044466918050058

References: PDF file   HTML file

English version:
Computational Mathematics and Mathematical Physics, 2018, 58:5, 700–713

Bibliographic databases:

UDC: 519.633
Received: 27.12.2016

Citation: A. V. Boiko, K. V. Demyanko, Yu. M. Nechepurenko, “Numerical analysis of spatial hydrodynamic stability of shear flows in ducts of constant cross section”, Zh. Vychisl. Mat. Mat. Fiz., 58:5 (2018), 726–740; Comput. Math. Math. Phys., 58:5 (2018), 700–713

Citation in format AMSBIB
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    This publication is cited in the following articles:
    1. K. V. Demyanko, “O vremennoi ustoichivosti techeniya Puazeilya v kanale ellipticheskogo secheniya”, Preprinty IPM im. M. V. Keldysha, 2018, 278, 25 pp.  mathnet  crossref
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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