  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 nonlinear
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.
