一种寻求层状流动新解的方法

A METHOD FOR EXPLORING SOME NEW SOLUTIONS OFLAMELLAR FLOW

复杂层状流动是流体力学中的一类典型的流动．一般而言,流体力学中有两种特殊的流动:一种是Beltrami流动,另一种就是层状流动．对于前者,已经讨论过很多;但是后者的精确解却很难获得,这是因为很难解这种流动的Navier-Stokes方程或Euler方程．从不可压缩条件出发,如果让速度的形式满足一些特殊的条件,可以得到关于这种流动的某些新的精确解,例如发现一种间歇流精确解．

Complex lamellar flow is a typical flow in fluid mechanics. Its research has significanttheoretical and applied value. Generally speaking, there are two special flows in nature: one isthe Beltrami flow defined by ω=λu; another is the lamellar flow satisfying ω. u = 0. We havelearned much about the former flow. But the solutions of the latter are hard to obtain becauseof difficulties in solving the corresponding Navier-Stokes equation or Euler equation. From theincompressible condition, if we let the form of the velocity field satisfy some special conditions, wemay obtain some new solutions of this kind of lammellar flow by using different coordinate systems,including the rectangular coordinate system and axisymmetric cylindrical coordinate system. Forexample, we have found an exponential shear flow solution, an exact intermittent flow solution andan axisymmetric jet flow solution. The intermittent flow solution is found for the first time. Webelieve that the present work provides some implications which will be helpful for us to understandmore about this kind of flow and seek for more interesting solutions.