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تسجيل مستخدم جديدSpatial decay of the vorticity field of time-periodic viscous flow past a body
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We study the asymptotic spatial behavior of the vorticity field, $omega(x,t)$, associated to a time-periodic Navier-Stokes flow past a body, $mathscr B$, in the class of weak solutions satisfying a Serrin-like condition. We show that, outside the wake region, $mathcal R$, $omega$ decays pointwise at an exponential rate, uniformly in time. Moreover, denoting by $bar{omega}$ its time-average over a period and by $omega_P:=omega-bar{omega}$ its purely periodic component, we prove that inside $mathcal R$, $bar{omega}$ 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 $mathscr B$, $omega(x,t)$ behaves like the vorticity field of the corresponding steady-state problem.
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