常曲率窄深型弯曲河流水流动力稳定特征理论研究

Instability of laminar flow in narrow and deep meander channel with constant curvature

弯曲型河流是自然界最为常见的河流形态,河道中河床形态和河势单元的发展与水流流态转化密切相关.作为这方面的研究基础,以常曲率窄深型河流(河湾)为背景,对流动稳定性特征进行了研究,得到了弯道层流理论计算公式和临界雷诺数计算公式,对于弯道设计具有指导作用.与顺直河道相比,其稳定中性曲线沿坐标轴前移,失稳临界雷诺数增加,对扰动波数的响应范围减小,流动状态更易保持,为进一步研究河湾"点沙坝"和"自由沙坝"等河势单元的形态形成打下理论基础,丰富了非线性河流动力学理论.

The meander river is the one of the most common type in natural river morphology.Its flow pattern influences transformation and development of river morphology.A preliminary theory of the transition from laminar to turbulent flow in a narrow and deep meander channel with constant curvature is investigated in this paper.A new velocity distribution formula of laminar flow and a formula of critical Reynolds number against bend curvature were found.These formulas will be valuable to bend channel design.The analyses on relevant parameters reveal that the curvature can play an important part in flow stability.The neutral curve will move rightward and the critical Reynolds number increase with bank curvature increasing.The flow is unstable in response to a narrower range of disturbance wave number;therefore,the flow can maintain stability as laminar flow.These results establish the fundamental theory to further study ＇point bar＇ and ＇free bar＇ in meandering rivers.