The cause was chronic lymphomic leukemia, said his son Peter.
Fluid dynamics, a subject that concerns the physics of what happens when a cup of coffee is stirred, when moisture from the sides of a rain-soaked truck flies into the windshield of a trailing car, when air passes over an airplane wing or when a storm front passes through a mountain range, is the study of how liquids and gases behave in motion. Dr. Orszag, who had taught at Yale since 1998 and before that at Princeton and the Massachusetts Institute of Technology, was especially interested in problems of turbulent flow — that is, the complications that result when the flow is especially rapid and irregular, for example when a brisk stream encounters a bridge pillar.
It is a field both fundamental to life on earth — not to mention the rest of the universe — and devilishly complicated, but the practical applications are both huge and timely. To name just one, simulation models of air and water flow over the chassis of cars and trucks can give designers clues for reducing drag — and thus saving vast amounts of fuel.
“To explain the pattern of a vigorously stirred cup of coffee, to express mathematically, in detail, how all the fluid particles move around in the cup, something that is apparently banal, is a major scientific feat,” said John S. Wettlaufer, a colleague of Dr. Orszag’s at Yale, where he is a professor of geophysics, physics and applied mathematics.
The mathematical expressions that underlie the dynamics of fluids, turbulent or otherwise, comprise a set of differential equations for fluid velocity that are reliant on factors like viscosity, density and gravity. Known as the Navier-Stokes equations, they reflect Newton’s second law of motion — that is, force equals mass times acceleration — and their generality allows them to describe a vast range of liquid behaviors, “from pouring honey on your toast,” Dr. Wettlaufer said, “to feeling a gust of air on your face on a windy day.”
Dr. Orszag greatly advanced the study of these equations by developing new methods for solving them, known as spectral methods. The complexities of the work led him to the development of new methods of computing, which were specifically devised to help with the difficulties of creating mathematical models of turbulent flow situations. Dr. Orszag’s advances made problem-solving in the field exponentially faster and more accurate.
Steven Alan Orszag was born in Manhattan on Feb. 27, 1943, and grew up in Forest Hills, Queens. His father was a lawyer. A precocious intellect, he entered M.I.T. at 16 and graduated at 19. He attended St. Johns College at Cambridge, in England, and earned a Ph.D. in astrophysics from Princeton at 23.
“The joke about him was that he was the youngest person ever to turn 40,” said his son Peter, a vice chairman of global banking at Citibank who is a former budget director for President Obama and a former contributing columnist to The New York Times’s Op-Ed Page.
After a year at the Institute of Advanced Studies in Princeton, N.J., Dr. Orszag joined the faculty at M.I.T. in 1967 before returning to Princeton in 1984. He was the author of a number of books, including a widely used textbook, written with Carl Bender, “Advanced Mathematical Methods for Scientists and Engineers.” And his research led him to help found or become chief scientific adviser to a number of companies, including Ibrix, a data storage company that was bought by Hewlett-Packard in 2009, and Exa, which develops simulation software for fluids engineering companies.
Dr. Orszag lived in New Haven and Princeton. In addition to his son Peter, who lives in New York and Washington, he is survived by his wife, the former Reba Karp, whom he married in 1964; a sister, Myrna Baron of Scottsdale, Ariz.; two other sons, Jonathan, of Los Angeles, and Michael, of London; and two grandchildren.
This article has been revised to reflect the following correction:
Correction: May 7, 2011
An earlier version of this obituary incorrectly referred to Dr. Orszag's wife, Reba, as Reva.
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