The evolution of a wall-attached plume in a confined box is studied here with the aid of three dimensional direct numerical simulations (DNS). The plume originates from a local line heat source of length, L, placed at the bottom left corner of the box. The Reynolds number of the wall plume, based on box height and buoyant velocity scale, is ${\mathit{Re}}_H=14530$ and boxes of two different aspect ratios (ratio of box width to height) for a particular value of L are simulated. We observe that the plume develops along the vertical sidewall while remaining attached to it before spreading across the top wall to form a buoyant fluid layer and eventually moving downwards and filling the whole box. The original filling box model of Baines and Turner (1969) is modified to incorporate the wall shear stress, and the results from the DNS are compared against the new model. In modelling plumes, we find that the entrainment coefficient ($\alpha$) for wall-attached plumes is reduced to approximately half of that in the free plume, and the main reason is a diminished contribution of turbulence production to $\alpha$ resulting from a restricted ability of the large-scale eddies to transport momentum. Also, unlike the free plume where away from the source inertial forces balances buoyancy forces, here in our simulations of wall-attached plumes this balance is marginally off, likely due to wall friction. A reasonable agreement is observed between our model and DNS data for the volume and momentum fluxes in the quiescent uniform environment and also for the time-dependent buoyancy profile calculated far away from the plume.

此处借助三维直接数值模拟 (DNS) 研究了密闭箱中附壁羽流的演变。羽流源自放置在盒子左下角的长度为L的局部线热源。基于箱体高度和浮力速度标度的壁羽的雷诺数为${\mathit{关于}}_H=14530$并且针对特定的L值模拟了两种不同纵横比（框宽度与高度之比）的框。我们观察到羽流沿着垂直侧壁发展，同时保持附着在它上面，然后扩散到顶壁形成一个浮力流体层，最终向下移动并填充整个盒子。Baines 和 Turner (1969) 的原始填充盒模型经过修改以包含壁面剪应力，并将 DNS 的结果与新模型进行比较。在建模羽流时，我们发现夹带系数 ($\alpha$) 壁挂羽流减少到自由羽流中的大约一半，主要原因是湍流产生对 $\alpha$由于大尺度涡流传递动量的能力受限。此外，与远离源惯性力平衡浮力的自由羽流不同，在我们对附着在壁上的羽流的模拟中，这种平衡略微偏离，可能是由于壁面摩擦。在我们的模型和 DNS 数据之间，对于静止均匀环境中的体积和动量通量以及远离羽流计算的时间相关浮力剖面，观察到合理的一致性。