Mixing Closures for Conservation Laws in Stratified Flows
Mixing Closures for Conservation Laws in Stratified Flows
复制标题
分层流中守恒定律的混合闭包
DOI：
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
E. Tabak
中科院分区：
文献类型：
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作者：
T. Jacobson;P. Milewski;E. Tabak
给出了两层分层流动中流体混合激波的闭合形式。闭合使混合速度最大化，将动态水力方程和熵条件作为约束条件。这种闭合也可以被视为通过内部激波产生混合速率的上限。结果表明，最大混合率是由激波以允许的最快速度向上游流动运动实现的。根据限制这一速度的主动约束是松弛熵条件还是能量正耗散，我们精确地区分了内部水力跳跃和钻孔。最大化夹带被证明等同于最大化与混合有关的适当的熵。通过使用后者，可以通过优化过程来描述全局流动，而不需要单独处理激波。建立了一个通用的数学框架，当守恒定律的数量不足时，可以用最大化原理来补充。
A closure for shocks involving the mixing of the fluids in two‐layer stratified flows is proposed. The closure maximizes the rate of mixing, treating the dynamical hydraulic equations and entropy conditions as constraints. This closure may also be viewed as yielding an upper bound on the mixing rate by internal shocks. It is shown that the maximal mixing rate is accomplished by a shock moving at the fastest allowable speed against the upstream flow. Depending on whether the active constraint limiting this speed is the Lax entropy condition or the positive dissipation of energy, we distinguish precisely between internal hydraulic jumps and bores. Maximizing entrainment is shown to be equivalent to maximizing a suitable entropy associated to mixing. By using the latter, one can describe the flow globally by an optimization procedure, without treating the shocks separately. A general mathematical framework is formulated that can be applied whenever an insufficient number of conservation laws is supplemented by a maximization principle.