Journal of Samara State Technical University, Ser. Physical and Mathematical SciencesJournal of Samara State Technical University, Ser. Physical and Mathematical SciencesВестник Самарского государственного технического университета. Серия «Физико-математические науки»1991-86152310-7081Samara State Technical University4199110.14498/vsgtu1766ArticlesСтатьиResearch ArticleExact solutions to generalized plane Beltrami–Trkal and Ballabh flowsТочные решения обобщенных плоских течений Бельтрами–Тркала и БеллабаProsviryakovEugenii YurevichПросвиряковЕвгений Юрьевич

Doctor of physico-mathematical sciences, no status

доктор физико-математических наук, без звания

evgen_pros@mail.ruInstitute of Engineering Science, Urals Branch, Russian Academy of SciencesИнститут машиноведения УрО РАН31072020242VOL 24, NO2 (2020)ТОМ 24, №2 (2020)31933004082020Copyright ©; 2020, Samara State Technical UniversityCopyright ©; 2020, Самарский государственный технический университет2020Samara State Technical UniversityСамарский государственный технический университетhttps://creativecommons.org/licenses/by/4.0https://journals.eco-vector.com/1991-8615/article/view/41991

Nonstationary plane flows of a viscous incompressible fluid in a potential field of external forces are considered. An elliptic partial differential equation is obtained, with each solution being a vortex flow stream function described by an exact solution to the Navier–Stokes equations. The obtained solutions generalize the Beltrami–Trkal and Ballabh flows. Examples of such new solutions are given. They are intended to verify numerical algorithms and computer programs.

Рассмотрены плоские нестационарные течения вязкой несжимаемой жидкости в потенциальном поле внешних сил. Получено уравнение в частных производных эллиптического типа, каждое решение которого является функцией тока вихревого течения, описываемого некоторым точным решением уравнений Навье–Стокса. Полученные решения обобщают течения Бельтрами–Тркала и Беллаба. Даны примеры таких новых решений. Они предназначены для верификации численных алгоритмов и компьютерных программ.

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