Fine characterization of wind drag force in shallow lakes based on the wind-wave-flow mutual feedback model

Water environment pollution and water ecological degradation are the common problems in lake. As the dynamic basis of lake system, lake hydrodynamics has a decisive influence on lake water environment and water ecology. The numerical simulation is an important means to study the characteristics of lake hydrodynamics, water environment and water ecology. For numerical simulation of lakes driven by wind, the drag force of airflow on water is usually represented by wind drag coefficient ( C_d ). C_d reflects the momentum transfer efficiency between water and airflow, and is closely related to the characteristics of wind，waves，flow and their mutual feedback mode, and is the most critical parameter to determine whether the numerical simulation results are reasonable. However, the expression methods of wind drag coefficient widely used at present are mostly proposed based on the ocean. The characteristics of ocean wind, wave, flow and their mutual feedback mode are less affected by the blowing range and water depth. C_d is mainly restricted by wind speed ( u₁₀ ) without considering the influence of the blowing range ( F ) and water depth( d ), which has poor adaptability in lakes.

In this study, theoretical analysis, wind tunnel experiment, in-situ monitoring and numerical simulation were used to propose a model of wind-water interaction in finite water area considering the wind-wave-flow mutual feedback model. Two dimensionless numbers, u₁₀/(gF)^0.5and u₁₀F/ν_w, which can be used to describe the comprehensive strength of wind-wave and wind-flow interaction in finite water area were constructed. A new expression of wind stress coefficient considering wind speed, blow distance and water depth is proposed (expression (1) ), which improves the limitation of the traditional expression considering wind speed only, overcomes the limitation of its application in limited blow distance and water depth, and maintains the overall consistency with the existing expression. When the wind speed is greater than 5m/s, the wind stress coefficient is positively correlated with u₁₀ and F, and negatively correlated with d，the sensitivity of the three factors to the C_d is 0.92, 0.22 and 0.14, respectively. The results of the three dimensional hydrodynamic mathematical model of Lake Tai show that the simulation results of the wind stress coefficient considering the influence of three factors are more consistent with the measured results.