中文摘要：

对流动控制方程即连续方程、动量方程和能量方程进行坐标转化，将带有自由表面和不平坦底面的不规则物理区域转变为规则的矩形计算区域。应用大涡模拟Smagorinsky模型对控制方程进行模化，根据破裂算子法将动量方程和能量方程分解成对流、扩散和传播三步进行顺序求解。利用该模型对静止和规则波环境下二维窄缝热浮力射流进行数值模拟，比较了两种环境下速度场、温度场、轴线速度衰减规律、垂向流速的自相似分布等特性，分析了浮力的作用以及射流速度、窄缝宽度等因素对射流掺混过程中温度场分布的影响。数值模拟结果得到已有理论及试验成果的验证。

英文摘要：

A three-dimensional numerical model of the coordinate is developed. The z-coordinate transformation transfers the irregular physical domain with the wavy free surface and uneven bottom to the regular computational domain with the shape of rectangular prism. The Smagorinsky model is used in the modeling. The operator splitting method, breaking the solution proce- dure into the advection, diffusion, and propagation steps, is used to solve the modified Navier-Stokes equations and energy e- quation. The model is used to simulate thermal buoyant jets in both stagnant water and wave environment, to compare the dis- tribution of velocity and temperature, the decay law of the mean velocity along axis and the self-similar characteristic, and to numerically analyze the influence factors such as the width of slot and the difference of temperature. The numerical result is of great practical importance for the design of the thermal and wastewater diffusers.