Summary
It is suggested that long-range correlation in a rarefied gas can be described by a hierarchy of generalized Boltzmann equations which, unlike either the Liouville equation or the BBGKY hierarchy, take the rarefaction of the gas into account and are presumably easier to handle. The equations are postulated, and compatibility criteria for their truncation as well as a class of truncations are proposed. The work presented here can be regarded as a further step toward a kinetic theory of turbulence (for rarefied gases) along the lines of Zhigulev and Tsugé.
Riassunto
Si suggerisce che correlazioni a lungo raggio in un gas rarefatto possono essere descritte da una gerarchia di equazioni di Boltzmann che, diversamente sia dall'equazione di Liouville che dalla gerarchia BBGKY, tengono conto della rarefazione del gas e sono presumibilmente piú facili da usare. Si postulano le equazioni e si propongono i criteri di compatibilità per i loro troncamenti e una classe di troncamenti. Il lavoro presentato qui può essere considerato come un ulteriore passo verso una teoria cinetica della turbolenza (per gas rarefatti) sulla linea di Zhigulev e Tsugé.
Резюме
Предполагается, что дальнодействующие корреляции в разреженном газе могут быть описаны с помощью иерархии обобщенных уравнений Больцмана, которые, в отличие от уравнения лиувилля или иерархии ББГКИ, учитывают разрежение газа и с которыми легче обращаться. Постулируются уравнения и предлагаются критерии совместимости для их обрезания, а также класс обрезаний. Эта работа может рассматриваться как дальнейший шаг в кинетической теории турбулентности (для разрежеддых газов).
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The work was supported by the Air Force Office of Scientific Research, United States Air Force, under Grant. No. AFOSR-71-2053 and grant A4825 from the Natural Sciences and Engineering Research Council, Canada.
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Sastri, C.C.A. Compatibility criteria for generalized Boltzmann equations. Nuov Cim B 77, 42–48 (1983). https://doi.org/10.1007/BF02738417
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DOI: https://doi.org/10.1007/BF02738417