For decades, scientists who study hurricanes,
whirlpools and other large fluid vortices have puzzled over
precisely how these vast swirling masses of gas or liquid
sustain themselves. How do they acquire the energy to keep
moving? The most common theory sounded like it was lifted
from Wall Street: The large vortices collect power as
smaller vortices merge and combine their assets, in the
same way that small companies join forces to create a mega
corporation.
But researchers from Johns Hopkins and
Los Alamos National
Laboratory now believe the better model is a much
different business tactic: the hostile takeover. Working
with theoretical analysis, computer simulations and lab
experiments, the team has concluded that large fluid
vortices raid their smaller neighbors in an energy grab and
then leave their depleted victims either to wither away or
to renew their resources by draining still smaller
vortices.
The findings were published in the March 3 issue of
the journal Physical Review Letters. "This discovery
is important because it could lead to a better
understanding of how hurricanes and large ocean eddies
form," said
Shiyi Chen, an
author of the paper. "It should also help us to create
better computer models to make more accurate predictions
about these conditions."
Chen is a professor in Johns Hopkins'
Department of Mechanical
Engineering, where he holds the Alonzo G. Decker Jr.
Chair in Engineering and Science. He supervised the
computer simulations in this two-and-a-half-year research
project.
The team looked at large energetic vortex structures
that form in irregular or turbulent two-dimensional flows
of gas or liquid. Common examples are the Red Spot on
Jupiter and hurricanes or typhoons on Earth. The
researchers wanted to figure out how energy is transferred
from smaller vortices to these large-scale circulation
patterns. The basic phenomenon, called "inverse energy
cascade," was predicted almost 40 years ago by pioneering
turbulence theorist Robert H. Kraichnan. However, the
dynamical mechanism underlying the inverse cascade has
remained obscure. Does it occur, as some scientists
suggested, through a merger of small vortices to form a new
larger one?
"We went into this with an open mind, but we found
that the popular idea of mergers was not correct," said
Gregory Eyink,
a Johns Hopkins professor of
applied mathematics and
statistics and currently the 2006 Ulam Scholar at Los
Alamos Laboratory's Center for Nonlinear Studies.
He said the energy transfer actually occurs through a
process described as a "thinning mechanism."
"You have a large vortex spinning around, with a
smaller one inside," Eyink said. "The large vortex has a
shearing effect on the smaller one, like cake batter being
stirred. The large-scale vortex acts like a giant mixer,
stretching and thinning out the smaller one, transferring
its energy into the larger vortex. The large-scale vortex
actually acts like a vampire, sucking the energy out of the
smaller one."
This phenomenon sustains a steady-state inverse energy
cascade. "We end up with a group of large predator vortices
preying on smaller ones, which in turn prey on smaller ones
still, forming a food chain of vortices," Eyink said.
Through computer modeling at Johns Hopkins and
laboratory experiments at Los Alamos on thin saltwater
layers, the scientists were able to observe the physical
processes and measure the energy transfer. This confirmed
their theory that an energy transfer by stretching of
small-scale vortices is what sustains large-scale
vortices.
Robert Ecke, director of the Center for Nonlinear
Studies at Los Alamos, an author of the journal article and
supervisor of the lab experiments, said, "This is the first
time a quantitative connection has been made between the
process of vortex thinning and inverse energy cascade."
The team's research was supported by grants from the
National Science Foundation and the U.S. Department of
Energy. Co-authors are Michael Rivera, of the Los Alamos
Materials Science and Technology Division, and Minping Wan
and Zuoili Xiao, both graduate students in the Department
of Mechanical Engineering at Johns Hopkins.