Anomalous Dissipation in Passive Scalar Transport
Anomalous Dissipation in Passive Scalar Transport
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DOI：
10.1007/s00205-021-01736-2
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发表时间：
2022-01-16
影响因子：
2.5
通讯作者：
Jeong, In-Jee
中科院分区：
文献类型：
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作者：
Drivas, Theodore D.;Elgindi, Tarek M.;Jeong, In-Jee
我们研究被动标量背景下流体动力湍流的反常耗散。我们的主要结果产生了一个不可压缩的 C-无穷大 ([0, T) x T-d ) 布尔 AND L-1 ([0, T]; C1-(T-d)) 速度场，该速度场明确表现出反常耗散。因此，该示例还显示了具有不可压缩 L-1 ([0, T]; C1- (T-d)) 漂移的输运方程解的非唯一性，该方程除了在某个时间点外都是平滑的。我们还基于无粘方程的解以受控方式变为奇异的方式给出了反常耗散的充分条件。最后，我们讨论与标量湍流的 Obukhov-Corrsin 单分形理论的联系以及其他潜在应用。
We study anomalous dissipation in hydrodynamic turbulence in the context of passive scalars. Our main result produces an incompressible C-infinity ([0, T) x T-d ) boolean AND L-1 ([0, T]; C1-(T-d)) velocity field which explicitly exhibits anomalous dissipation. As a consequence, this example also shows the non-uniqueness of solutions to the transport equation with an incompressible L-1 ([0, T]; C1- (T-d)) drift, which is smooth except at one point in time. We also give a sufficient condition for anomalous dissipation based on solutions to the inviscid equation becoming singular in a controlled way. Finally, we discuss connections to the Obukhov-Corrsin monofractal theory of scalar turbulence along with other potential applications.