快猫短视频

LORD Rayleigh, modern fluid dynamicists, and readers of New
快猫短视频 all have something in common: they鈥檝e all been wrong about how
flags flap.

Ever since the 18th century people have believed that a flag must flap even
in the softest breeze, because the slightest imperfections in the flag鈥檚 surface
creates swirling vortices in the passing air. These vortices make the flag
billow out, creating more vortices and even more billows. This was how readers
of 快猫短视频鈥檚 The Last Word answered the question 鈥淲hat makes a
flag flutter?鈥�
(18 December 1999).

But physicists Jun Zhang and Michael Shelley of New York University and their
colleagues say a flag should fly straight in a breeze鈥攑roviding it鈥檚 not
too long and gravity doesn鈥檛 interfere. 鈥淏efore, people believed that only the
American flag on the Moon, which is a sheet of aluminum in no atmosphere, can
stand straight out,鈥� Zhang says. 鈥淏ut even a flag in a fluid can do it.鈥�

The findings may shed light on how flowing fluids interact with pliant
objects and surfaces ranging from the wings of insects to the walls of blood
vessels, says Greg Huber, a physicist at the University of Massachusetts,
Boston. 鈥淭he physics of flags is not something that many people care about,鈥� he
says, 鈥渂ut they do care about blood flowing in the heart and fluid flowing
around microorganisms.鈥�

To make things simpler, the researchers needed to reduce the number of
dimensions, so they dangled a one-dimensional flag鈥� a thin
filament鈥攊n a film of soapy water held between two vertical cords. The
film flowed downwards between the cords under the force of gravity. In order to
see the film flowing, the researchers shone a light on it to pick out the
irridescent interference patterns visible on soap films.

The researchers varied the length of the filament to see how it would affect
the flapping. The filament stayed straight and produced a straight trail of
vortices when it was less than roughly 2.3 centimetres. Between 2.3 and 4
centimetres, however, it would either remain straight or flap and spawn a
sinuous stream of vortices. Any filament more than 4 centimetres long always
flapped.

Catching a real flag flat and motionless may be tricky because gravity tends
to make flags cumple up and hang down in weak breezes, says Maarten Rutgers, a
physicist at Ohio State University in Columbus. 鈥淲hat you really should be
looking at is a flag that has no gravity acting on it,鈥� he says, 鈥渙r a flag
hanging straight down with a wind blowing down on it.鈥�

Researchers and fans of the Last Word who have argued that a non-flapping
flag is impossible can take comfort鈥攖he problems of fluid flow over
movable surfaces are deceptively tricky, Huber says. 鈥淭hey鈥檙e harder than they
appear to be at first,鈥� he says, 鈥渁nd this is a prime example.鈥�