A plane turbulent mixing in a shear flow of an ideal homogeneous fluid confined between two relatively close rigid walls is considered. The character of the flow is determined by interaction of vortices arising at the non-linear stage of the Kelvin–Helmholtz instability development and by turbulent friction. In the framework of the shallow water theory and a three-layer representation of the flow, one-dimensional models of a mixing layer are proposed. The obtained equations allow one to determine averaged boundaries of the region of intense fluid mixing. Stationary solutions of the governing equations are constructed and analysed. Using the averaged flow characteristics obtained by one-dimensional equations, a hyperbolic system for determining the velocity profile and Reynolds shear stress across the mixing layer is derived. Comparison with the experimental results of the evolution of turbulent jet flows in a Hele–Shaw cell shows that the proposed models provide a fairly accurate description of the average boundaries of the region of intense mixing, as well as the velocity profile and Reynolds shear stress across the mixing layer.

考虑了限制在两个相对紧密的刚性壁之间的理想均质流体的剪切流中的平面湍流混合。流动的特性取决于开尔文-亥姆霍兹不稳定性发展的非线性阶段中产生的涡流的相互作用以及湍流摩擦。在浅水理论和流动的三层表示的框架下，提出了混合层的一维模型。所获得的方程式允许确定强烈流体混合区域的平均边界。构造并分析了控制方程的平稳解。使用通过一维方程式获得的平均流动特性，推导了用于确定混合层上的速度分布和雷诺剪切应力的双曲线系统。