
ALEXANDRE CHORIN

BERKELEY, CA — For more than 30 years, Dr.
Alexandre Chorin has worked to develop computational methods for solving
problems in fluid mechanics, with the hope that they will eventually lead
to an understanding of the most difficult problem of applied mathematics
 the problem of turbulence.
What makes the turbulence problem so compelling, in addition to its
practical importance, Chorin says, is that the basic equations that
describe turbulence are well known and simple, yet their solutions are
incredibly complex and the computing power needed to find them transcends
any imaginable computer.
Chorin, who holds a joint appointment as a senior scientist at the U.S.
Department of Energy’s Lawrence Berkeley National Laboratory and a
professor of mathematics at UC Berkeley, has developed a number of methods
for studying fluid flow since the mid1960s. This work has been absorbed
into the mainstream of research, yet it has not been sufficient for
solving the problem of turbulent fluid flow. Chorin and his collaborators
continue to explore new ways of tackling the problem, and their work
continues to be acknowledged as critically important.
Most recently, the Society for Industrial and Applied Mathematics and
the Applied Mathematics Society honored Chorin earlier this year with the
2000 Norbert Wiener Prize, one of the highest distinctions in applied
mathematics. The prize citation states that Chorin received the prize
"in recognition of his seminal work in computational fluid dynamics,
statistical mechanics, and turbulence. His work has stimulated important
developments across the entire spectrum from practical engineering
applications to convergence proofs for numerical methods..."
Chorin will discuss his work in an April 5 lecture entitled "How
to Put the Guesswork Back into Computing." His talk will begin at 4
p.m. in the Wheeler Auditorium on the UC Berkeley campus.
From the 1960s to the present day, Chorin has led and inspired applied
mathematicians everywhere to tackle the most difficult realworld problems
and to make full use of the combined power of advanced computers and
sophisticated mathematical analysis. In the process, he has done more than
anyone else to create and shape the important discipline of computational
applied mathematics.
Chorin points out that his recent work has been done jointly with a
number of collaborators, noted mathematicians as well as risingstar
students, and that his work incorporates their many contributions. Yet his
leadership is also widely acknowledged; in addition to the latest prize,
he is in his third year as Chancellor’s Professor of Mathematics and has
just been elected by the UC Berkeley Academic Senate as one of two Campus
Research Lecturers.
And although he is gratified by the recognition of his past efforts, he
is more interested in the work at hand: the new method of optimal
prediction which he hopes will contribute to the solution of the
turbulence problem, and scaling methods that explore hidden structures in
turbulence through the analysis of experimental data.
Turbulence is the seemingly random behavior of a fluid which occurs all
over nature, in the atmosphere, the oceans, the interior of stars and
inside internal combustion chambers. Being able to accurately compute
turbulence has a wide range of applications, from predicting tornadoes to
designing aircraft, from improving industrial processes to building more
efficient boilers. As an engineering student with a love of cars and
airplanes, Chorin became interested in turbulence as it affects lift (the
force that keeps aircraft aloft) and drag (the resistance of air to the
motion of cars and planes). In short, turbulence has the power to make
vehicles run  or not run.
Turbulence provides Chorin with a problem that combines his interest in
physics, mathematics and computation. Turbulence is extraordinarily
mystifying, he says. It looks like a problem in physics, but it isn’t.
"We have known the equations of motion for nearly two centuries and
in principle they contain all the information one needs, except we don’t
know how to extract answers from these equations," Chorin said.
"The physicists have done their job; the mystery is
mathematical."
In fact, Chorin said that scientists today are better able to explain
the structure of stars than accurately predict turbulence in a liquid
flowing through a pipe.
One may think that the way to solve the problem is through computation,
as is the case with many other problems in fluid motion; but trying to
determine the structure of a turbulent flow in a typical application may
take as many as 10tothepower80 mathematical operations  assuming
that the chaotic nature of the solution does not interfere too much and
that a way can be found to gather and understand the output from such a
computation.
The problem totally defeats any presentday supercomputer, as well as
any currently conceivable computer, Chorin says. It is too complex, too
long. However, it would be extraordinarily interesting to find a way to
tame the complexity.
What makes the problem so complex, he says, is that it is a
multidimensional problem, and that it contains many different scales of
motion, like a weather map, which contain patterns that cover entire
continents and patterns that affect small regions, maybe a street corner.
All these motions are coupled and affect each other; none can be neglected
when one tries to understand what is happening.
Chorin and his collaborators, including Grigory Barenblatt, who also
holds a joint appointment at Berkeley Lab and UC Berkeley, have come up
with two ideas which they believe could lead to some progress.
The first is a new attack on the problem of scaling  the uncovering
of relations between motion on different scales in a problem that contains
many scales. Using new mathematical tools and recent experimental data,
Chorin and Barenblatt discovered new scaling relations, some of which
overthrew earlier assumptions that had been widely used in engineering and
aeronautics work since the 1930s.
Scaling laws are examples of general, useful relations that can be used
and understood even without a detailed solution of the equations of
motion.
The second idea Chorin and his collaborators (in particular, Prof. Ole
Hald of the UC Berkeley Mathematics Department, Prof. Raz Kupferman of
Jerusalem, and Drs. Anton Kast and Doron Levy of Berkeley Lab) have been
developing goes under the name of "optimal prediction."
The equations that describe turbulence are general principles,
asserting such obvious truths as the conservation of mass and energy. What
one tries to do on the computer is extract from these equations detailed
properties of flows in specific situations  for example, the weather on
a given day or the flow in a specific combustion chamber. This goal is
unachievable. However, before one undertakes a calculation one knows a lot
of "prior information": general mathematical, physical and
statistical principles provide information about what kinds of solutions
are likely to appear, and scaling laws and sheer experience provide other
hints.
The idea in optimal prediction is to lower one's sights: settle not for
a full, certain solution, but for the most likely solution that can be
found, given the prior information and a preset, maybe modest, amount of
computation. This approach, which may have wide applicability in other
complex problems, is being tried on turbulence, and while it has not yet
succeeded, Chorin is hopeful.
This is clearly a work in progress, but if successful, optimal
prediction could prove useful in research areas ranging from biology to
economics  any complex problem with some data, but far more unknowns
than can be conventionally calculated.
Berkeley Lab is a U.S. Department of Energy National Laboratory located
in Berkeley, California. It conducts unclassified scientific research and
is managed by the University of California.
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