Abstract: A three-dimensional numerical model of the coordinate is developed The σ-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 splitt ing method,breaking the solution procedure into the advection,diffusion,and propagat ion steps,is used to solve the modified Navier-Stokes equations and energy equation The model is used to simulate thermal buoyant jets in both stagnant water and wave environment,to compare the distribution 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.