Summary
A singular perturbation method is used to find the stream function within the critical layer, which matches to the inviscid singular neutral solution which is valid outside the critical layer. The fluid is assumed to be incompressible and stratified. Also the connection between the inviscid solution on the two sides of the critical layer is given for all values ofR c, the Richardson number at the critical layer. It is found that arg (U−c)=−π whenU−c<0if arg (U−c)=0 whenU−c>0.
Zusammenfassung
Eine singuläre Störungsrechnung wird zur Bestimmung des an die reibungsfreie, singuläre, neutrale, außerhalb der kritischen Schicht gültigen Lösung anschließenden Strömungspotentials in der kritischen Schicht verwendet. Das Fluid wird als inkompressibel und geschichtet angenommen. Angegeben wird auch die Verknüpfung mit der reibungsfreien Lösung zu beiden Seiten der kritischen Schicht für alle Werte vonR c' der Richardson-Zahl der kritischen Schicht. Es zeigt sich, daß arg (U−c)=−π fürU−c<0 wenn arg (U−c)=0 fürU−c>0.
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Engevik, L. The stream function within the critical layer of a shear flow in a stratified and incompressible fluid. Acta Mechanica 19, 169–178 (1974). https://doi.org/10.1007/BF01176484
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DOI: https://doi.org/10.1007/BF01176484