Buoyancy-driven exchange flows occur in a variety of natural and industrial situations, including nuclear and hydraulic engineering, oceanography and building ventilation. Balanced exchange flows, whereby there is simultaneously an equal volume flux transferred vertically upwards and downwards through a horizontal opening, have previously been described theoretically. However, until now there has been no theoretical description of unbalanced exchange flows, whereby the volume flux in one direction through an opening exceeds that in the other. The model developed herein examines the growth of perturbations on the density interface at an opening made in a horizontal plane that connects buoyant fluid below with denser fluid above. By considering the interface as it is advected away from the plane of the opening by a bulk flow imposed in the vertical, we quantify the exchange for the unbalanced case. The model successfully predicts the Froude number criterion, which corresponds directly to the minimum dimensionless flow rate of the imposed flow, for the onset of unbalanced exchange across circular openings found experimentally. Additionally, comparisons made between the exchanges predicted and measured show excellent agreement across the entire range of possible flows, from unidirectional flow, through unbalanced exchange to balanced exchange. Consideration is given to applications of the model to ocean outfall design and to the prediction of building ventilation flows. For natural ventilation, the theoretical model we derive for unbalanced exchange bridges the gap in the prediction of air flow rates between displacement flows, where the flow is unidirectional, and balanced exchange flows.

中文翻译：

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通过水平开口的浮力驱动的不平衡交换流

浮力驱动的交换流发生在各种自然和工业环境中，包括核和水利工程、海洋学和建筑通风。平衡交换流，其中同时有相等的体积通量通过水平开口垂直向上和向下转移，先前已在理论上进行了描述。然而，直到现在还没有不平衡交换流的理论描述，即通过开口的一个方向的体积通量超过另一个方向的体积通量。此处开发的模型检查了密度界面上的扰动的增长，该界面位于水平面中的开口处，该开口将下方的浮力流体与上方的密度较大的流体连接起来。通过考虑由于垂直施加的整体流而远离开口平面的界面，我们量化不平衡情况下的交换。对于实验发现的圆形开口之间不平衡交换的开始，该模型成功地预测了弗劳德数准则，该准则直接对应于施加流的最小无量纲流速。此外，预测和测量的交换之间的比较表明，从单向流到不平衡交换到平衡交换的整个可能流量范围都非常一致。考虑了该模型在海洋排放口设计和建筑物通风流量预测中的应用。对于自然通风，我们为不平衡交换推导出的理论模型弥补了置换流（其中流动是单向的）和平衡交换流之间的空气流速预测中的差距。