Exact Solutions to Navier–Stokes Equations Describing a Gradient Nonuniform Unidirectional Vertical Vortex Fluid Flow

The paper announces a family of exact solutions to Navier–Stokes equations describing gradient inhomogeneous unidirectional fluid motions (nonuniform Poiseuille flows). structure the motion is such that incompressibility equation enables us establish velocity defect law for nonuniform flow. In this case, field dependent on two coordinates and time, it an arbitrary-degree polynomial relative horizontal (longitudinal) coordinate. coefficients depend vertical (transverse) coordinate time. solution under consideration was built using method indefinite use algebraic operations addition multiplication. As result, determine coefficients, we derived system simplest homogeneous parabolic partial equations. order integration resulting recurrent. For special case steady flows viscous fluid, these are ordinary differential article presents algorithm their integration. all components field, vorticity vector, shear stress functions. addition, has been noted even without taking into account thermohaline convection (creeping current) fields have rather complex structure.