Theorie Schallnaher Strömungen
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Schallnahe Stromungen sind dadurch gekennzeichnet, daB inner- halb des Stromungsfeldes gleichzeitig Uberschall- und Unterschall- gebiete auftreten. Die tiefgehende Verschiedenheit diesel' Stromungs- typen ist die Ursache fUr mancherlei Schwierigkeiten, die bei del' Behandlung schailnaher Stromungen auftreten. Wirklich uberwunden sind diese Schwierigkeiten keineswegs, z. B. ist die scheinhar einfache Frage nach del' Druckverteilung an einem gegebenen Profil im schall- nahen Gebiet bisher nicht befriedigend beantwortet worden. Tat- sachlich versucht die Theorie schallnaher Stromungen in erster Linie, die grundlegenden Eigenschaften und V organge zu verstehen, und verzichtet - notgedrungen - auf die genaue Vorhersage von Einzel- heiten. Selbst dieses beschrankte Programm erfordert einige V orsicht. Sowohl fur Unterschallstromungen als auch fur Uberschallstromungen gibt es analoge physikalische Vorgange, die zur Veranschaulichung dienen konnen. AuBerdem ist die nahe Verwandtschaft del' Differential- gleichungen mit del' LAPLACEschen Gleichung im Unterschall und mit del' Wellengleichung im Uberschall auBerst wertvoll. Gleiches trifft fUr schallnahe Stromungen nicht zu, es gibt fast keine den gemischten Stromungen analoge Phanomene, und die vorhandene Theorie del' gemischt-elliptischhyperbolischen Differentialgleichungen, so wertvoll sie ist, reicht fur die Beantwortung del' grundlegenden mathematischen Fragen nicht vollig aus. So kann man sich in diesen Untersuchungen kaum auf das physi- kalische GefUhl odeI' auf Plausibilitatsbetrachtungen verlassen. Fur den Verfasser bedeutet das allerdings nieht, daB man rein formal vorgehen solIte; im Laufe del' Beschaftigung mit exakt gewonnenen Beispielen und durch sorgfaltige Diskussion del' Erscheinungen laBt sich auch fUr die Phanomene del' schallnahen Stromungen ein Anschauungs- vermogen entwickeln, das eine Extrapolation del' Ergebnisse tiber das Exakt-Bekannte hinaus ermoglicht.
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