Characteristics and material transport of a bubble-driven plume in stably stratified water with uniform crossflow are studied using an Eulerian-Eulerian large-eddy simulation model. Four laboratory-scale plume conditions with different bubble rise velocities ($w_r=3$, 6, 12, and $20\mathrm{cm}/\mathrm{s}$) are considered, and their characteristics under three weak crossflow conditions ($U_c=0.5$, 1, and $2\mathrm{cm}/\mathrm{s}$) are studied. The interaction between the rising bubbles and the stratified water generates a double-plume structure, consisting of a rising plume of bubble/water mixture and a falling plume of dense water peeled from the rising plume due to the stratification effect. The presence of crossflow forces the rising plume to incline and causes the falling plume to form on the downstream side (with respect to the crossflow direction) of the rising plume, resulting in reduced contact area between the two plumes. Consequently, the turbulent mixing of the vertical momentum between the rising and falling plumes is reduced, causing the magnitude of the vertical velocity in both plumes to increase when the crossflow velocity is increased. The material transport from the plume to the horizontal intrusion layer (traced using dye) also exhibits strong dependence on the crossflow velocity. Faster crossflow results in narrower lateral extension and wider vertical extension of the intrusion layer due to the interaction between the peeling process and the crossflow. For cases with the two smaller $w_r$ (3 and $6\mathrm{cm}/\mathrm{s}$), the plume can form a distinct peeling event that dominates the material transport process. As a result, the mean intrusion layer height $h_t$ shows only small variation for these two plume conditions when $U_c$ is increased. In contrast, the plumes with $w_r=12$ and $20\mathrm{cm}/\mathrm{s}$ exhibit noticeable decrease of $h_t$ ($9\%$ and $24\%$, respectively) when $U_c$ is increased from $0.5$ to $2\mathrm{cm}/\mathrm{s}$. Statistical analysis of the streamwise dye flux shows that the decrease of $h_t$ with increased $U_c$ for the cases with $w_r=12$ and $20\mathrm{cm}/\mathrm{s}$ is mainly due to the crossflow-enhanced mean flux of dye from the rising plume at the low elevation.

中文翻译：

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分层错流中气泡羽流的大涡模拟

利用Eulerian-Eulerian大涡模拟模型研究了气泡在稳定分层水中具有均匀横流的气泡驱动羽状流的特性和物质传输。四种实验室规模的羽状条件，具有不同的气泡上升速度（$w_{\mathrm{[R}}=3$，6、12和 $20\mathrm{厘米}/\mathrm{s}$），并在三种弱横流条件（${ü}_C=0.5$，1和 $\mathrm{2个}\mathrm{厘米}/\mathrm{s}$）进行研究。上升的气泡与分层水之间的相互作用产生了双泡沫结构，该结构由泡沫/水混合物的上升羽流和由于分层效应而从上升羽流剥离的浓水下降羽流组成。横流的存在迫使上升的羽流倾斜并且导致下降的羽流在上升的羽流的下游侧（相对于横流方向）形成，导致两个羽流之间的接触面积减小。因此，上升的和下降的羽流之间的垂直动量的湍流混合减少了，当横流速度增加时，两个羽流中的垂直速度的大小也增加了。从羽流到水平侵入层（使用染料追踪）的物质传输也表现出对横流速度的强烈依赖性。由于剥离过程和错流之间的相互作用，更快的错流导致侵入层的横向扩展更窄，垂直扩展更宽。对于两个较小的情况$w_{\mathrm{[R}}$ （3和 $6\mathrm{厘米}/\mathrm{s}$），羽流会形成明显的剥落事件，从而主导物料的运输过程。结果，平均入侵层高度$H_{Ť}$ 当这两个羽状条件出现时，仅显示很小的变化 ${ü}_C$增加。相反，羽状带$w_{\mathrm{[R}}=12$ 和 $20\mathrm{厘米}/\mathrm{s}$ 表现出明显的下降 $H_{Ť}$ （$9％$ 和 $24％$分别）何时 ${ü}_C$ 从增加 $0.5$ 至 $\mathrm{2个}\mathrm{厘米}/\mathrm{s}$。对沿流染料流量的统计分析表明，$H_{Ť}$ 随着增加 ${ü}_C$ 对于有的情况 $w_{\mathrm{[R}}=12$ 和 $20\mathrm{厘米}/\mathrm{s}$ 这主要是由于在低海拔地区，上升的羽状流产生的交叉流增强了平均染料通量。