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Dear authors! Submission of all materials is carried out only electronically through Online Submission System in personal account. DOI: 10.23671/VNC.2016.4.5994 On the Problem of Shear Flow Stability with Respect to LongWave Perturbations
Revina S. V.
Vladikavkaz Mathematical Journal 2016. Vol. 18. Issue 4.
Abstract:
To find secondary flow branching to the steady flow it is necessary to consider linear spectral problem and linear adjoint problem. Longwave asymptotics of linear adjoint problem in twodimensional case is under consideration. We assume the periodicity with spatial variables when one of the periods tends to infinity. Recurrence formulas are obtained for the $k$th term of the velocity and pressure asymptotics. If the deviation of the velocity from its periodaverage value is an odd function of spatial variable, the velocity coefficients are odd for odd $k$ and even for even \(k\). The relations between coefficients of linear adjoint problem and linear spectral problem are obtained.
Keywords: stability of twodimensional viscous flows, longwave asymptotics, linear adjoint problem
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