非惯性非正交曲线坐标系中的边界层方程

BOUNDARY LAYER EQUATIONS IN NONINERTIAL CURVILINEAR COORDINATE SYSTEM

应用张量分析方法将 N- S方程写于作非惯性运动的非正交曲线坐标系中 ,然后用匹配渐近展开法导出此坐标系中的边界层方程。消去压强项后 ,与惯性坐标系中的边界层方程相比 ,非惯性系中的边界层方程在 x1和 x2 方向的动量方程中分别只多了一哥氏力项 ,它们是由物体转动角速度的物面法向分量产生的 ,其它惯性力项均不进入边界层方程。方程中所含曲线坐标系的拉梅系数及其导数只需在物面上取值 。

The boundary layer equations in a noninertial curvilinear coordinate system are derived using the technique of asymptotic expansion. As the pressure terms are eliminated from the first order boundary layer equations, only one Coriolis force term appears in the x 1 and x 2 momentum equations (they are due to the local normal component of the angular velocity of the moving body), while other inertial force terms do not enter the first order boundary layer equations