A. Nold

For the last decades, hydrodynamic stability theory has been vastly studied using the normal-mode approach leading to the well-known Orr-Sommerfeld Equation. Though rather successful for boundary layer flows it essentially failed for internal canonical flows such as the channel, Couette or pipe flow. In order to generate new approaches which are inherently given in the mathematical formulation of the problem, we apply symmetry methods on the linearized Navier-Stokes Equation (LNSE) for nearly parallel shear flows with two-dimensional perturbations. In particular, we show that the Orr-Sommerfeld-Equation is a symmetry reduction using the full set of symmetries for unrestricted base flows. We found that restricting the base flow to a special profile, the LNSE admits further symmetries, which we present in the context of a complete symmetry classification. Especially the algebraic, the exponential, the logarithmic and the linear shear flow admit additional symmetries, for which we present new solutions of the perturbations which are very distinct from the normal mode solution. In particular, we show that the generally known solution for the stability problem of linear viscous base flows is based on a symmetry reduction, too. We give an alternative formulation to this solution, using a different set of symmetries. For an inviscid linear shear flow, we give a simple formulation of a solution consisting of stable self-similar modes.

Deutscher Luft- und Raumfahrtkongress 2010

Conference Paper

englisch

21,0 x 29,7 cm, 7 Seiten

Deutscher Luft- und Raumfahrtkongress Tagungsband - Manuskripte, 2010, 2010, ; S.441-447; 2010; Deutsche Gesellschaft für Luft- und Raumfahrt - Lilienthal-Oberth e.V., Bonn

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Bestellbar

2010