Abstract
The nonlinear stability of time-periodic Poiseuille Flow is investigated using the Energy Theory. The time dependency in the basic flow is obtained by periodic modulation of the ground temperature. Energy stability limits, obtained by a combination of Galerkin and Floquet methods, are lowered by the thermal modulation. For both strong and mean energy formulations, the effect of increasing the modulation amplitude is to destabilize the flow which is demonstrated by a decrease in the stability boundary. A shift in the critical wavenumber due to modulation is also observed.
Zusammenfassung
Die nicht-lineare Stabilität der zeitlich periodischen Poiseuille-Strömung wird mittels Energiemethoden untersucht. Die Zeitabhängigkeit wird mit Hilfe einer periodischen Modulation der Grundtemperatur erhalten. Die Energie-Stabilitätsgrenze, die durch eine Kombination von Galerkin- und Floquet-Methoden erhalten wurde, wird durch die thermische Modulation heruntergesetzt. Sowohl für die starke wie auch für die mittlere Energie-Formulierung ist der Effekt der zunehmenden Energie-Amplitude eine Abnahme der Stabilität; dabei wird auch eine Änderung der kritischen Wellenzahl beobachtet.
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A major portion of this work comprises part of the doctoral thesis of R. C. Shulze.
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Shulze, R.C., Carmi, S. Energy stability of thermally modulated Poiseuille flow. Z. angew. Math. Phys. 34, 583–595 (1983). https://doi.org/10.1007/BF00948803
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DOI: https://doi.org/10.1007/BF00948803