Abstract
Unsteady pseudo-plane and plane motions for Navier-Stokes equations have been studied, which are generalized Beltrami flows, related to separable stream functions. All the pseudo-plane motions of the first kind of such a type, a wide class of plane universal solutions, which seems to be new, and a class of pseudo-plane motions of the second kind, dependent on an arbitrary function of time, with a primitive steady plane solution which is the celebrated Kelvin's cat's eye vortices are formed.
Sommario
Si studiano moti non stazionari pseudopiani e piani dell'equazioni di Navier Stokes. Questi moti sono flussi generalizzati di Beltrami con una particolare dipendenza della funzioni di corrente dalle coordinate spaziali in modo separato. Nell'ambito di questa famiglia di flussi vengono esplicitamente trovati tutti i moti pseudopiani di primo tipo e vengono anche individuate un'ampia classe di soluzioni universali piane e una classe di moti pseudopiani del secondo tipo che possiedono come flussoprimitivo i famosi vortici adocchi di gatto di Kelvin.
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Saccomandi, G. Some unsteady exact pseudo-plane solutions for the Navier-Stokes equations. Meccanica 29, 261–269 (1994). https://doi.org/10.1007/BF01461439
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DOI: https://doi.org/10.1007/BF01461439