Dresden 2009 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 25: Fluid dynamics II

DY 25.4: Talk

Thursday, March 26, 2009, 15:30–15:45, ZEU 118

On the parametric resonances of layered immiscible fluids — •Bernhard Heislbetz — DLR Lampoldshausen, Institut für Raumfahrtantriebe, D-74239 Hardthausen, Germany

As a generalization of the well known Faraday-Instability of a free fluid surface, we theoretically investigate the parametric resonances of stratified immiscible fluid layers under the action of an external time periodic excitation.

Considering the full viscous hydrodynamic system, we show that the dynamics of the interface between two layers of viscous fluids can be reduced to an equation of the Mathieu-type, including several temporal non-local memory integrals. Due to analytical approximations and numerical calculations we characterize the the stability behaviour of a parametrically excited interface between two fluid layers of arbitrary viscosity.

Furthermore we discuss the stability problem for the interfaces of a three-layer configuration. Within the framework of ideal fluids the temporal evolution of the interface deformations are governed by coupled Mathieu differential equations. Including fluids viscosity, we show that the interfacial dynamics is determined by a set of coupled integro-differential equations. Resonant instability domains associated to the stability of subharmonic and harmonic solutions of the problem were calculated using Floquet Theory. The characteristics of the obtained stability zones were explained by means of a multiple-time scale analysis.