Summary
Finite amplitude steady convection in a horizontal layer of fluid heated from below with nearly insulating boundaries and rotating about a vertical axis is investigated. The main result is that the only steady stable convective motion in the form of square pattern becomes unstable once the rotation parameter τ exceeds the value 7.45. The disturbances which have the highest growth rates are in the form of rolls inclined at an angle of 45° to the basic wave vectors of the steady motion.
Zusammenfassung
Das Problem der stationären Konvektion endlicher Amplitude wird untersucht für eine horizontale von unten erhitzten Flüssigkeitsschicht, die um eine vertikale Achse rotiert. Das Hauptresultat ist, daß die einzige stabile stationäre Konvektionsströmung in der Form von Quadratzellen instabil wird, wenn der Rotationsparameter τ den kritischen Wert 7.45 übersteigt. Die Strömungen höchster Anwachsrate haben die Form von Rollen, die einen Winkel von 45° mit den Wellenzahlvektoren der stationären Lösung einschließen.
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References
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Riahi, N. Convection in a rotating layer with nearly insulating boundaries. Z. angew. Math. Phys. 33, 81–92 (1982). https://doi.org/10.1007/BF00948314
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DOI: https://doi.org/10.1007/BF00948314