The heuristic Fermi-Neumann box model is used to study the non-Boussinesq lock exchange flows in an infinite horizontal channel. This allowed us to find the asymptotic growth laws for intrusion tongues at a late stage of their development. It is shown that these laws are essentially different. The classical scenario of the linear growth x1∝t is supported only by the lower (heavy) intrusion tongue. The same is not true for the upper (light) intrusion tongue that obeys the law x2∝t/lnt.

中文翻译：

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锁交换流中入侵舌的渐近增长规律

启发式 Fermi-Neumann 盒模型用于研究无限水平通道中的非 Boussinesq 锁交换流。这使我们能够在入侵舌头的发展后期找到渐近增长规律。可见，这些规律本质上是不同的。线性增长 x1∝t 的经典场景仅由下部（重）侵入舌支撑。对于遵守定律 x2∝t/lnt 的上（轻）侵入舌，情况并非如此。