We report an experimental investigation of turbulence in bubble plumes released in unstratified quiescent water. The focus is to study the detailed turbulent statistics and the budget terms in the equations of turbulent kinetic energy (TKE), particularly about their distributions in the radial direction of bubble plumes compared to those in the single-phase momentum jets and buoyant plumes. Two types of diffusers were used to generate plumes consisting of different bubble sizes and population at the same source gas discharge. The bubble plumes have different growth behaviors under different combination of sizes and population: the plumes with many small bubbles show decreasing centerline velocities along the vertical direction; the plumes with larger but fewer bubbles have a tighter bubble core, a smaller spreading ratio, and almost constant centerline velocities. The ratio of turbulence-to-mean in momentum flux is strongly affected by bubble sizes and population, demonstrated in the profiles of normalized turbulent velocity correlations using mean flow parameterizations. Velocity fluctuations show a strong vertical-to-horizontal anisotropy in bubble plumes compared to those in single-phase jets and plumes. Strong vertical fluctuating velocity component contributes a significant role in re-shaping the radial profiles of turbulent stresses and transport terms when the bubble plume is composed of larger but fewer bubbles. Local balance cannot be established in the equation of TKE traditionally used for single-phase flows. A bubble-related source term in the governing equation is needed to close the budget. An empirical equation using drag force and bubble slip velocity is validated for the TKE closure. We provide a diagram of TKE budget to illustrate the pathway of TKE terms in the radial direction, with the magnitude of each term influenced by bubble characteristics.

我们报告了在未分层静止水中释放的气泡羽流湍流的实验研究。重点是研究湍流动能方程（TKE）中详细的湍流统计和预算项，特别是与单相动量射流和浮力羽流相比，它们在气泡羽流径向的分布。两种类型的扩散器用于在相同的源气体排放处产生由不同气泡大小和数量组成的羽流。气泡羽流在不同大小和种群的组合下有不同的生长行为：气泡多的羽流沿垂直方向的中心线速度呈递减趋势；具有较大但较少气泡的羽流具有更紧密的气泡核心，更小的扩散率，和几乎恒定的中心线速度。动量通量中湍流与平均值的比率受气泡大小和数量的强烈影响，这在使用平均流参数化的归一化湍流速度相关性的轮廓中得到了证明。与单相射流和羽流相比，气泡羽流的速度波动显示出强烈的垂直到水平各向异性。当气泡羽流由较大但较少的气泡组成时，强大的垂直波动速度分量在重塑湍流应力和传输项的径向轮廓方面起着重要作用。在传统上用于单相流的 TKE 方程中无法建立局部平衡。需要控制方程中与泡沫相关的源项来关闭预算。使用阻力和气泡滑移速度的经验方程验证了 TKE 闭合。我们提供了一个 TKE 预算图来说明 TKE 项在径向上的路径，每个项的大小受气泡特征的影响。