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A generalisation of Prandtl's model for 3D open channel flows

The paper presents generalisation of the old Prandtl mixing-length hypothesis (MLH) for three-dimensional (3D) flows to provide engineers with a new tool to calculate the mean velocity distribution in turbulent open channel flows. These flows are usually not isotropic, i.e. turbulence may have different length scales in different directions. Hence, at every point of the flow a symmetrical second-order tensor with dimension of length should be given. The components of this tensor are specified based on the structure of the largest turbulent eddies. To demonstrate the usefulness of the proposed model, the Reynolds equations with the new turbulence model are solved and calculated streamwise velocity contours are compared with the measurement results. The importance of turbulent structure (sizes of the largest eddies and their growth rate) in forming the streamwise velocity contours is shown.