Journal
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
Volume 242, Issue 1, Pages 149-178Publisher
SPRINGER
DOI: 10.1007/s00205-021-01690-z
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The study focuses on the asymptotic spatial behavior of the vorticity field associated with a time-periodic Navier-Stokes flow past a body, showing exponential decay outside the wake region and faster decay inside it. This implies that the vorticity field behaves like that of the corresponding steady-state problem sufficiently far from the body.
We study the asymptotic spatial behavior of the vorticity field, omega(x, t), associated to a time-periodic Navier-Stokes flow past a body, B, in the class of weak solutions satisfying a Serrin-like condition. We show that, outside the wake region, R, omega decays pointwise at an exponential rate, uniformly in time. Moreover, denoting by (omega) over bar its time-average over a period and by omega P := omega - (omega) over bar its purely periodic component, we prove that inside R, (omega) over bar has the same algebraic decay as that known for the associated steady-state problem, whereas omega P decays even faster, uniformly in time. This implies, in particular, that sufficiently far from B, omega(x, t) behaves like the vorticity field of the corresponding steady-state problem.
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