2 results
Search Results
Now showing 1 - 2 of 2
- ItemViscous Flow Around a Rigid Body Performing a Time-periodic Motion(Cham (ZG) : Springer International Publishing AG, 2021) Eiter, Thomas; Kyed, MadsThe equations governing the flow of a viscous incompressible fluid around a rigid body that performs a prescribed time-periodic motion with constant axes of translation and rotation are investigated. Under the assumption that the period and the angular velocity of the prescribed rigid-body motion are compatible, and that the mean translational velocity is non-zero, existence of a time-periodic solution is established. The proof is based on an appropriate linearization, which is examined within a setting of absolutely convergent Fourier series. Since the corresponding resolvent problem is ill-posed in classical Sobolev spaces, a linear theory is developed in a framework of homogeneous Sobolev spaces.
- ItemSpatial decay of the vorticity field of time-periodic viscous flow past a body(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2020) Eiter, Thomas; Galdi, Giovanni P.We study the asymptotic spatial behavior of the vorticity field associated to a time-periodic Navier-Stokes flow past a body in the class of weak solutions satisfying a Serrin-like condition. We show that outside the wake region the vorticity field decays pointwise at an exponential rate, uniformly in time. Moreover, decomposing it into its time-average over a period and a so-called purely periodic part, we prove that inside the wake region, the time-average has the same algebraic decay as that known for the associated steady-state problem, whereas the purely periodic part decays even faster, uniformly in time. This implies, in particular, that ``sufficiently far'' from the body, the time-periodic vorticity field behaves like the vorticity field of the corresponding steady-state problem.