Chaotic fluid mixing in non-quasi-static time-periodic cavity flows

Fluid mixing in a two-dimensional square cavity with a time-periodic pulsating lid velocity is studied. A spectral element technique for spatial discretization is combined with a continuous projection scheme for temporal discretization to obtain a numerical representation of the non-quasi-static velocity field in the cavity. It is well known that mixing in a cavity with a steady lid velocity results in linear mixing of fluid inside the cavity. Here, it is shown that superposition of a pulsating component on the steady lid velocity can lead to chaotic mixing in the core of the cavity. An extra steady motion of the opposite cavity wall, resulting in a small perturbation to the original flow, causes the chaotically mixed region to be spread over almost the whole cavity. Poincare and periodic point analysis reveal the main characteristics for these transient time-periodic flows, and elucidate the details and properties of the chaotic mixing in these flows.