每年出版 6 期
ISSN 打印: 2152-5102
ISSN 在线: 2152-5110
Indexed in
Exact Solutions of Three-Dimensional Transient Navier − Stokes Equations
摘要
Exact solutions to Navier − Stokes equations are rare due to its inherently nonlinear nature. Most of the known solutions are highly simplified and are obtained by eliminating certain terms. In case of three-dimensional transient Navier − Stokes equations, for all known solutions nonlinear part is zero. Nonlinear part of Navier − Stokes equations plays important role in various phenomena like convection and turbulent energy transfer. For some known axisymmetric and two-dimensional solutions nonlinear term is not zero but it is linearized. In this paper new type of solutions are obtained in which nonlinear part is not linearized and their nonlinearity is preserved. Solutions presented in this paper are believed to be first ever 3D nonlinear solutions of the Navier − Stokes equations for incompressible fluid. General solution of 2D Navier − Stokes equations for stream function homogeneous in space is obtained in the paper. These 2D solutions are used to enrich the obtained nonlinear 3D solutions. The sole purpose of this paper is to present new kinds of exact solutions, to help researchers trying to understand and explore physics of fluid motion.