LINEAR GLOBAL INSTABILITY OF THE PLANE FLOW WITH MEANDERING WALL

In the hydrodynamic and processing research of meandering river, it is implicitly assumed that the relationship between secondary flow and secondary turbulence is the same as that between mean flow and turbulence in open channel flows. However, there is no relevant turbulence research to support this implicit assumption, due to the limitation of DNS model and PIV measurement at high Reynolds number. The differences and similarities research of turbulent structures development between meandering channel and straight channel flow are benefit to the secondary turbulent flow in meandering rivers. A planar two-dimensional NS equation in orthogonal coordinate system and the two-parameter perturbation method were established to solve the weak nonlinear laminar flow and flow instability problem in the meandering channel. And a governing equation, named with extended Orr-Sommerfeld (EOS) equation was derived to solve the eigenvalue problem of planer flow with meandering boundary. The weak nonlinear laminar flow is combination of a series of meandering harmonic components, in which the linear component causes the velocity difference between the two walls, and the nonlinear component increases exponentially with the increase of Reynolds number. The first modal of the disturbance growth rate spectrum is similar to that of the straight channel flow, which is composed of three type curves and divided four disturbance wave bands. However, the disturbance flow field at the longwave band and the shortwave band is different from that of the straight flow. Specially, the velocity disturbance at shortwave band is similar to that of the Kelvin-Helmholtz vortex, may due to the velocity difference caused by linear component of laminar. The two meandering parameters have a certain selectivity to the internal disturbance in channel. The larger the angular amplitude is, the faster the disturbance grows. With the increase of the meandering wavenumber, the disturbance growth rate increases at first and then decreases. The disturbed flow field is formed by superposition of a typical TS wave and a pair of wave packets. The wave packet pair has only longitudinal velocity components, with two envelopes controlled by the boundary wavenumber and interior TS wave with the same parameters as TS wave in the wave packet.