Author:
HALL PHILIP,PAPAGEORGIOU DEMETRIOS T.
Abstract
The flow between parallel walls driven by the time-periodic oscillation of one of
the walls is investigated. The flow is characterized by a non-dimensional amplitude
Δ and a Reynolds number R. At small
values of the Reynolds number the flow is
synchronous with the wall motion and is stable. If the amplitude of oscillation is held
fixed and the Reynolds number is increased there is a symmetry-breaking bifurcation
at a finite value of R. When R is further
increased, additional bifurcations take place,
but the structure which develops, essentially chaotic flow resulting from a Feigenbaum
cascade or a quasi-periodic flow, depends on the amplitude of oscillation. The flow in
the different regimes is investigated by a combination of asymptotic and numerical
methods. In the small-amplitude high-Reynolds-number limit we show that the flow
structure develops on two time scales with chaos occurring on the longer time scale.
The chaos in that case is shown to be associated with the unsteady breakdown of a
steady streaming flow. The chaotic flows which we describe are of particular interest
because they correspond to Navier–Stokes solutions of stagnation-point form. These
flows are relevant to a wide variety of flows of practical importance.
Publisher
Cambridge University Press (CUP)
Subject
Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics
Cited by
24 articles.
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