It
seems perfectly natural to expect that two motorists who depart from
the same location and follow the same directions will end up at the same
destination. But according to a Johns Hopkins University mathematical
physicist, this is not true when the “directions” are provided by a
turbulent fluid flow, such as you find in a churning river or stream.
Verifying earlier theoretical predictions, Gregory Eyink’s computer
experiments reveal that, in principle, two identical small beads dropped
into the same turbulent flow at precisely the same starting location
will end up at different – and entirely random – destinations.
“This
result is as astonishing and unexpected as if I told you that I fired a
gun aimed at precisely the same point on a target but the bullet went
in a completely different direction each and every time. It’s surprising
because, even though the beads are exactly the same and the flow of
water is exactly the same, the result is different,” said Eyink,
professor of applied mathematics and statistics at The Whiting School of
Engineering. “It is crucial here that the flow is turbulent — as in
whitewater rapids or a roiling volcanic plume — and not smooth, regular
flow as in a quiet-running stream.”
To
conduct his study, Eyink used a virtual “stream” that is part of an
online public database of turbulent flow created with Whiting School
colleagues Charles Meneveau and Randal Burns, as well as with physicist
Alexander Szalay of the Krieger School of Arts and Sciences. Into this
“stream” Eyink tossed virtual “particles” at precisely the same point
and let them drift within the fluid. The researcher then randomly
“kicked” each of the particles as they moved along, with different
“kicks” at different points along the way. The particles, as one would
expect when subjected to different “kicks,” followed different paths.
“But
here’s the surprising thing,” Eyink explained. “As the kicks got weaker
and weaker, the particles still followed random – and different –
paths. In the end, the computer experiment seemed to show that the
particles would follow different paths even if the kicks vanished
completely.”
This
phenomenon is called “spontaneous stochasticity,” which basically means
that objects placed in a turbulent flow – even objects that are
identical and which are dropped into the same spot – will end up in
different places.
“Thus,
we know that ‘God plays dice’ not only with subatomic particles, but
also with everyday particles like soot or dust carried by a turbulent
fluid,” Eyink said.
Eyink’s
study also revealed that the magnetic lines of force that are carried
along in a moving magnetized fluid (like a stream of molten metal) move
in a completely random way when the fluid flow is turbulent. This
contradicts the fundamental principle of “magnetic flux-freezing”
formulated by Nobel Prize-winning astrophysicist Hannes Alfvéen in 1942,
which states that magnetic lines of force are carried along in a moving
fluid like strands of thread cast into a flow.
“This
principle of Alfveen’s is fundamental to our understanding of how fluid
motions in the Earth’s core and in the sun generate those bodies’
magnetic fields, and my study may provide a solution to the longstanding
puzzle of why flux freezing seems to fail in violent solar flares and
in other turbulent plasma flows,” Eyink said.
This study was supported by the National Science Foundation.
Study abstract at Physical Review E
SOURCE: Johns Hopkins University
