Circulation-based models for Boussinesq internal bores
Circulation-based models for Boussinesq internal bores
复制标题
Boussinesq 内孔的基于循环的模型
DOI：
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发表时间：
2013
影响因子：
3.7
通讯作者：
E. Meiburg
中科院分区：
文献类型：
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作者：
Z. Borden;E. Meiburg
摘要 现有的用于预测内孔前沿速度的控制体积模型强制质量和流向动量守恒，但不强制垂直动量守恒。相反，他们通常引用与上游和下游能量通量相关的经验假设，以获得确定穿过孔的压力跃变所需的附加方程。目前的研究开发了一种仅基于质量和动量守恒的内孔控制体积模型，无需考虑能量。这是通过组合流向和垂直动量方程以获得不再涉及压力的涡度关系来实现的。因此，该涡度方程与质量守恒相结合足以评估孔速度。然后可以通过流向能量方程来预测整个孔的能量损失，并与早期模型的假设进行比较。新模型预测的内孔涡量通量与直接数值模拟结果非常一致。与实验测量的孔速度的任何差异都被证明是由于下游混合的影响造成的。
Abstract Existing control-volume models for predicting the front velocity of internal bores enforce the conservation of mass and streamwise momentum, but not vertical momentum. Instead, they usually invoke an empirical assumption relating the up- and downstream energy fluxes to obtain an additional equation required for determining the pressure jump across a bore. The present investigation develops a control-volume model for internal bores on the basis of mass and momentum conservation alone, without the need for considering energy. This is accomplished by combining the streamwise and vertical momentum equations to obtain a vorticity relation that no longer involves pressure. Hence, this vorticity equation, in combination with the conservation of mass, is sufficient for evaluating the bore velocity. The energy loss across the bore can then be predicted by the streamwise energy equation and compared to the assumptions underlying earlier models. The flux of vorticity across the internal bore predicted by the new model is seen to be in close agreement with direct numerical simulation results. Any discrepancies with experimentally measured bore velocities are shown to be due to the effects of downstream mixing.