## Exact solutions to generalized plane Beltrami-Trkal and Ballabh flows.(English)Zbl 1463.76032

Summary: 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.

### MSC:

 76F02 Fundamentals of turbulence 76M45 Asymptotic methods, singular perturbations applied to problems in fluid mechanics 76F45 Stratification effects in turbulence 76R05 Forced convection 76U05 General theory of rotating fluids 76D05 Navier-Stokes equations for incompressible viscous fluids
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