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яндекс.ћетрика

DOI: 10.23671/VNC.2016.4.5994

On the Problem of Shear Flow Stability with Respect to Long-Wave 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. Long-wave asymptotics
of linear adjoint problem in two-dimensional 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 period-average
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 two-dimensional viscous flows, long-wave asymptotics, linear adjoint problem
Language: Russian Download the full text  
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