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The News of Altai State University
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Content of 1(35) 2005
Mathematics and Computer Science

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A.M. Sagalakov, V.V. Chertishchev, V.V. Chertishchev

Search of periodic decisions of equation Navier-Stokes for currents in the flat channel

As a result of numerical modelling flat periodic fluid motions the decision of equation Navier-Stokes on the time interval amounting approximately 500÷2000 periods of natural time scale of flow, for R = 4000, α = 1,75; R = 5772, α = 1,25; R = 6000, α = 0,85 (precritical flow) and R = 5772, α = 1,025; R = 6000, α = 0,975; R = 6000, α = 1,020 (above-critical mode of flow) in the form of tables of Fourier factors, tables and images of lines of a flow. Perturbation in precritical modes of flow asymptotical aspired to zero. For above-critical modes by a method of an establishment are received quasi-periodical decisions in the form of a running wave. Period T for these modes appeared equal 2π / |Imλ1|, where λ1 is an eigenvalue of a linearized problem, having the maximal
material part.

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