Editor’s Challenge in Fluid Dynamics: Flows Across the Scales

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Spatio-temporal landscape of the leading-order physics in (i) the Oseen limit, Res1/2≪Rep<1, and (ii) the Saffman limit, Rep≪Res1/2<1. The triplets (◦, ◦, ◦) in the figure indicate the relative strengths of the inertial terms, in the order unsteady (|∂wd/∂t|), shear-advective (|wd ⋅∇u|), and slip-convective (|wd ⋅∇wd|) inertia, compared to the viscous terms (|∇2wd|∼|∇pd|). Asterisks denote dimensional quantities. Note in either limit, at later times, distinct “inner” and “outer” regions in space develop, and deviation from the standard kernel (Eqs. 5,6) is attributed to this. However, at short times, the diffusive unsteady Stokes equation drives the dynamics uniformly in space, yielding the standard Basset kernel. Idea courtesy: The schematic representation is inspired from Bentwich and Miloh [60] and Sano [59].
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Frontiers in Physics

Physics of Vortices and Vorticity in Flow Control
Edited by Xi Xia, Juan Li, Michael Krieg, Adam DeVoria, Chengyu Li
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18 June 2025
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