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Direction reversal and flapping in flightPDE and Applied Math Seminar
|Speaker: ||Saverio Spagnole, UCSD|
|Location: ||2112 MSB|
|Start time: ||Thu, Feb 5 2009, 3:10PM|
The dynamics of bodies immersed in ﬂuids is a sub ject of great practical and biolog-
ical interest. Fluid/body interaction systems are ubiquitous, ranging from large-scale
applications like swimming and ﬂying, to more recent work in the ﬁelds of microﬂuidic
devices, materials engineering, and micro-scale bioﬂuiddynamics. We will discuss two
such problems, motivated by recent experiments in the NYU Applied Math Lab.
First, in order to understand the role of ﬂexibility in ﬂapping ﬂight, we analyze
a heaving wing system with passive pitching. Experimental results are reproduced
qualitatively: we ﬁnd ﬂapping frequencies corresponding to very eﬃcient locomotion,
a regime of under-performance when compared to a rigid wing, and a bi-stable regime
where the ﬂapping wing can move either “forward” or “backward.” We ﬁnd that a
particular phase relationship corresponds to this direction reversal, and we consider
the importance of various dimensionless parameters.
Second, we will discuss a ﬂuid-ratchet mechanism that is exhibited by a shape-
changing body in an oscillating ﬂuid. We ﬁnd that such a body can maintain its
altitude, or even ascend, against a gravitational force. Simple analytical models are
shown to match the dynamics explored in numerical simulations. Other related phe-
nomena are also considered.