涡团模式及其流速分布公式对水力学学科的贡献OA

Prandtl's classical mixing-length theory and the logarithmic velocity-distribution law derived from it have long formed an important foundation for turbulence research.However,the assumption of a mixing length proportional to the distance from the boundary is not fully consistent with observed flow fields.In addition,the resulting logarithmic law has two major theoretical deficiencies:a mathematical singular-ity at the wall and a nonzero velocity gradient at the location of maximum velocity.Most existing modifications are based on local corrections or empirical fitting and have not resolved these problems simultaneously.Some of them also fail to provide an explicit analytical solution or a clear physical interpretation.Through theoretical analysis and validation against measured data,this study reviews the development and physi-cal basis of the turbulent eddy model,examines how it improves Prandtl's mixing-length theory,and evaluates the contributions of the model and its associated velocity-distribution formula to hydraulics in three areas:fundamental turbulence theory,flow-resistance calculation,and bend hydraulics.The results show that the turbulent eddy model is developed from the physical process of turbulent eddy motion and establi-shes a relationship between the rotational kinetic energy and gravitational potential energy of turbulent eddies.This relationship leads to a physically meaningful vertical distribution of the mixing length.The resulting velocity-distribution formula eliminates the wall singularity and satisfies the zero-gradient condition at the location of maximum velocity while retaining an explicit analytical form.To the authors'knowl-edge,the formula can accurately describe time-averaged velocity distributions and flow-resistance characteristics in clear-water and sediment-laden flows over hydraulically smooth and rough boundaries.Further developments based on the turbulent eddy model have produced analytical relationships for the vertical distribution and streamwise decay of bend secondary flow,its decay length,the near-bed flow direction,and the transverse water-surface slope.These results provide a new physically based and analytically tractable framework for turbulence research and its applications in hydraulics.