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arXiv 2407.01416physics.flu-dyn
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具有流向周期性的经典槽道流中阻力的Josephson-Anderson关系:壁面粗糙度的影响

A Josephson-Anderson relation for drag in classical channel flows with streamwise periodicity: Effects of wall roughness

Samvit Kumar, Gregory Eyink

AI总结:

本文将Josephson-Anderson关系推广到流向周期槽道,改用Dirichlet边界条件避免非物理涡片,证明压降瞬时功等于展向涡量积分通量,并用带光滑凸起的数值模拟揭示粗糙元涡分离与阻力、耗散的时空局部关联。

摘要:

详细的Josephson-Anderson关系将一般槽道任意流向段上压降所做的瞬时功与在该段上空间积分的展向涡量的壁面法向通量等同起来。这一关系最初由Huggins针对量子超流体导出,但它同样适用于经典流体的内部流动以及绕固体的外部流动,在后一类情形中对应于Burgers、Lighthill、Kambe、Howe等人的关系。所有这些先前的结果都采用一个与物理流动具有相同入流/出流条件的背景势Euler流,正如Kelvin最小能量定理中那样,因此参考势中包含了流动几何的信息。我们在此将详细的Josephson-Anderson关系推广到适用于经典流体湍流数值模拟的流向周期槽道。我们证明,Huggins为背景势所用的原始Neumann边界条件会在周期槽道中产生非物理的涡片,因此我们改用Dirichlet边界条件。我们证明最小能量定理仍然成立,并且我们新的Josephson-Anderson关系再次将压降所做的功瞬时等同于展向涡量的积分通量。该结果对Newton流体和非Newton流体以及一般曲线壁面均成立。我们用具有单个光滑凸起的周期槽道流的数值结果来说明我们的新公式,该结果揭示了粗糙元处的涡分离如何在每一时刻产生阻力。因此,阻力和耗散与涡量结构和动力学在空间和时间上局部相关,这对减阻以及解释高Reynolds数下的反常耗散具有重要应用。

英文摘要:

The detailed Josephson-Anderson relation equates instantaneous work by pressure drop over any streamwise segment of a general channel and wall-normal flux of spanwise vorticity spatially integrated over that section. This relation was first derived by Huggins for quantum superfluids, but it holds also for internal flows of classical fluids and for external flows around solid bodies, corresponding there to relations of Burgers, Lighthill, Kambe, Howe and others. All of these prior results employ a background potential Euler flow with the same inflow/outflow as the physical flow, just as in Kelvin's minimum energy theorem, so that the reference potential incorporates information about flow geometry. We here generalize the detailed Josephson-Anderson relation to streamwise periodic channels appropriate for numerical simulation of classical fluid turbulence. We show that the original Neumann b.c. used by Huggins for the background potential create an unphysical vortex sheet in a periodic channel, so that we substitute instead Dirichlet b.c. We show that the minimum energy theorem still holds and our new Josephson-Anderson relation again equates work by pressure drop instantaneously to integrated flux of spanwise vorticity. The result holds for both Newtonian and non-Newtonian fluids and for general curvilinear walls. We illustrate our new formula with numerical results in a periodic channel flow with a single smooth bump, which reveals how vortex separation from the roughness element creates drag at each time instant. Drag and dissipation are thus related to vorticity structure and dynamics locally in space and time, with important applications to drag-reduction and to explanation of anomalous dissipation at high Reynolds numbers.

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