Summary
The laminar boundary layer flow engendered by a rotating sphere is investigated using finite-difference approximations. The coordinate normal to the boundary layer is stretched to avoid the possibility of “cramping” the layer without having to use an inordinately large number of grid points. Variation of the step lengths enables the inaccuracies due to the finite-difference representations to be quantitatively assessed at each stage. The results are used to consider the details of the inviscid interaction at the equator where the eruption into a radial swirling jet occurs. The computation of the boundary layer is also continued beyond the equator and leads to a three-dimensional boundary-layer separation.
Zusammenfassung
Die durch eine rotierende Kugel hervorgerufene laminare Grenzschichtströmung wird mit Hilfe des Differenzenverfahrens untersucht. Die auf die Grenzschicht senkrecht stehende Koordinate wird dabei gestreckt um die Zahl der Gitterpunkte in erträglichen Grenzen zu halten. Eine Veränderung der Maschenweite erlaubt die Abschätzung der erzielten Genauigkeit bei jedem Schritt. Die Resultate werden zu einer Detailuntersuchung der reibungslosen Wechselwirkung am Äquator, wo ein Umschlag in einen radial wirbelnden Strahl erfolgt, verwendet. Die Berechnung der Grenzschicht wird auch über den Äquator hinaus fortgesetzt und führt zu einer dreidimensionalen Grenzschichtablösung.
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Banks, W.H.H. The laminar boundary layer on a rotating sphere. Acta Mechanica 24, 273–287 (1976). https://doi.org/10.1007/BF01190376
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DOI: https://doi.org/10.1007/BF01190376