Robert Kraichnan
Encyclopedia
Robert Harry Kraichnan a resident of Santa Fe
, New Mexico
, was an American
theoretical physicist
best known for his work on the theory of fluid turbulence
.
in Princeton
in 1949/50, and was one of the last assistants to Albert Einstein
.
After his appointment at Princeton, he worked in Columbia University
and the Courant Institute of Mathematical Sciences
at New York University
. From 1962 on, he was supported by research grants and worked as a freelance consultant for the Los Alamos National Laboratory
, Princeton University
, the Office of Naval Research
, the Woods Hole Oceanographic Institution
and NASA
. He had a keen passion for hiking, so he lived in the mountains of New Hampshire
s and later in White Rock, New Mexico
and eventually to Santa Fe, New Mexico
near Los Alamos
. In 2003, he returned to academia when he was appointed Homewood Professor in the Whiting School of Engineering
at Johns Hopkins University
, but by this time he had already fallen ill.
He was the recipient of the Onsager prize and the 1993 Otto Laporte Award
of the American Physical Society
, and the 2003 Dirac Medal. He was also a member of the National Academy of Sciences
.
Kraichnan married twice and has a son, John Kraichnan, by his first wife, Carol Gebhardt. He is also survived by his second wife, Judy Moore-Kraichnan, an artist and photographer who lives in Santa Fe. New Mexico
and the quantum mechanical
many-body problem
, developing starting in 1957 a method for finding a self-consistent formulation for many-body field theories, N-random-coupling-models, in which N copies of a microscopic theory are coupled together in a random way.
Following earlier work of Andrei Kolmogorov (1941), Lars Onsager
(1945), Werner Heisenberg
(1948), Carl Friedrich von Weizsäcker
and others on the statistical theory of Turbulence, Kraichnan developed a field-theoretic approach to fluid flow in 1957 derived from approaches to the quantum many-body problem--- the Direct Interaction Approximation. In 1964/5, he recast this approach in the Lagrangian picture , discovering a scaling correction which he had earlier incorrectly ignored. The statistical theory of turbulence in viscous liquids describes the fluid flow by a scale-invariant distribution of the velocity field, which means that the typical size of the velocity as a function of wavenumber is a power-law. In steady state, larger scale eddies at long wavelengths disintegrate into smaller ones, dissipating their energy into smaller length scales. This type of dissipation is not caused by friction on the molecular level, but by the nonlinear effects of the Navier Stokes equations. In the final stages of the energy cascade, at the smallest length scales, the viscosity becomes important and the energy dissipates into heat.
Kraichnan developed his turbulence theories over many decades and was one of the prominent American theorists in this area. From 1967 onwards, he maintained that for two-dimensional turbulence energy does not only dissipate itself from large scales (determined by the size of obstacles in the flow) to smaller ones as it does in three dimensions, but conversely that smaller fluctuations can increase in size. This theory is called the inverse Energy Cascade, and it is especially applicable to oceanography and meteorology, since flows on the surface of the earth are approximately two-dimensional. The theory was tested and confirmed in the 1980s by data gathered from weather balloons.
Also influential was a 1994 paper which presented an exactly solvable turbulence model, now called the Kraichnan model. This model predicts exactly computable anomalous scaling exponents for the advection
of a passive scalar field, like the concentration of a dye injected into the fluid which does not diffuse but moves with the fluid along the flow lines.
Even as a student, Kraichnan was busily investigating the general theory of relativity
, and his research won the prestigious Westinghouse Science Competition for students. He rewrote this work for his Bachelor thesis at MIT in 1947, titled "Quantum Theory of the Linear Gravitational Field" . Following an approach that was echoed by Suraj N. Gupta
, Richard Feynman
and Steven Weinberg
, Kraichnan showed that, under some mild secondary assumptions, the full nonlinear equations of general relativity follow from its linearized form: the quantum field theory
of a massless spin 2 particle, the graviton, coupled to the stress-energy tensor. The full nonlinear equations emerge when the energy-momentum of the gravitons themselves are included in the stress-energy tensor in a unique self-consistent way.
Santa Fe, New Mexico
Santa Fe is the capital of the U.S. state of New Mexico. It is the fourth-largest city in the state and is the seat of . Santa Fe had a population of 67,947 in the 2010 census...
, New Mexico
New Mexico
New Mexico is a state located in the southwest and western regions of the United States. New Mexico is also usually considered one of the Mountain States. With a population density of 16 per square mile, New Mexico is the sixth-most sparsely inhabited U.S...
, was an American
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
theoretical physicist
Theoretical physics
Theoretical physics is a branch of physics which employs mathematical models and abstractions of physics to rationalize, explain and predict natural phenomena...
best known for his work on the theory of fluid turbulence
Turbulence
In fluid dynamics, turbulence or turbulent flow is a flow regime characterized by chaotic and stochastic property changes. This includes low momentum diffusion, high momentum convection, and rapid variation of pressure and velocity in space and time...
.
Life
Kraichnan received his Ph.D. from MIT, graduating in 1949. He became a member of the Institute for Advanced StudyInstitute for Advanced Study
The Institute for Advanced Study, located in Princeton, New Jersey, United States, is an independent postgraduate center for theoretical research and intellectual inquiry. It was founded in 1930 by Abraham Flexner...
in Princeton
Princeton, New Jersey
Princeton is a community located in Mercer County, New Jersey, United States. It is best known as the location of Princeton University, which has been sited in the community since 1756...
in 1949/50, and was one of the last assistants to Albert Einstein
Albert Einstein
Albert Einstein was a German-born theoretical physicist who developed the theory of general relativity, effecting a revolution in physics. For this achievement, Einstein is often regarded as the father of modern physics and one of the most prolific intellects in human history...
.
After his appointment at Princeton, he worked in Columbia University
Columbia University
Columbia University in the City of New York is a private, Ivy League university in Manhattan, New York City. Columbia is the oldest institution of higher learning in the state of New York, the fifth oldest in the United States, and one of the country's nine Colonial Colleges founded before the...
and the Courant Institute of Mathematical Sciences
Courant Institute of Mathematical Sciences
The Courant Institute of Mathematical Sciences is an independent division of New York University under the Faculty of Arts & Science that serves as a center for research and advanced training in computer science and mathematics...
at New York University
New York University
New York University is a private, nonsectarian research university based in New York City. NYU's main campus is situated in the Greenwich Village section of Manhattan...
. From 1962 on, he was supported by research grants and worked as a freelance consultant for the Los Alamos National Laboratory
Los Alamos National Laboratory
Los Alamos National Laboratory is a United States Department of Energy national laboratory, managed and operated by Los Alamos National Security , located in Los Alamos, New Mexico...
, Princeton University
Princeton University
Princeton University is a private research university located in Princeton, New Jersey, United States. The school is one of the eight universities of the Ivy League, and is one of the nine Colonial Colleges founded before the American Revolution....
, the Office of Naval Research
Office of Naval Research
The Office of Naval Research , headquartered in Arlington, Virginia , is the office within the United States Department of the Navy that coordinates, executes, and promotes the science and technology programs of the U.S...
, the Woods Hole Oceanographic Institution
Woods Hole Oceanographic Institution
The Woods Hole Oceanographic Institution is a private, nonprofit research and higher education facility dedicated to the study of all aspects of marine science and engineering and to the education of marine researchers. Established in 1930, it is the largest independent oceanographic research...
and NASA
NASA
The National Aeronautics and Space Administration is the agency of the United States government that is responsible for the nation's civilian space program and for aeronautics and aerospace research...
. He had a keen passion for hiking, so he lived in the mountains of New Hampshire
New Hampshire
New Hampshire is a state in the New England region of the northeastern United States of America. The state was named after the southern English county of Hampshire. It is bordered by Massachusetts to the south, Vermont to the west, Maine and the Atlantic Ocean to the east, and the Canadian...
s and later in White Rock, New Mexico
White Rock, New Mexico
White Rock is a census-designated place in Los Alamos County, New Mexico, United States. The population was 6,045 at the 2000 census. It is largely a bedroom community for employees of Los Alamos National Laboratory and their families...
and eventually to Santa Fe, New Mexico
Santa Fe, New Mexico
Santa Fe is the capital of the U.S. state of New Mexico. It is the fourth-largest city in the state and is the seat of . Santa Fe had a population of 67,947 in the 2010 census...
near Los Alamos
Los Alamos, New Mexico
Los Alamos is a townsite and census-designated place in Los Alamos County, New Mexico, United States, built upon four mesas of the Pajarito Plateau and the adjoining White Rock Canyon. The population of the CDP was 12,019 at the 2010 Census. The townsite or "the hill" is one part of town while...
. In 2003, he returned to academia when he was appointed Homewood Professor in the Whiting School of Engineering
Whiting School of Engineering
The G.W.C. Whiting School of Engineering, is a division of the Johns Hopkins University located in the university's Homewood campus in Baltimore, Maryland, United States...
at Johns Hopkins University
Johns Hopkins University
The Johns Hopkins University, commonly referred to as Johns Hopkins, JHU, or simply Hopkins, is a private research university based in Baltimore, Maryland, United States...
, but by this time he had already fallen ill.
He was the recipient of the Onsager prize and the 1993 Otto Laporte Award
Otto Laporte Award
The Otto Laporte Award was an annual award by the American Physical Society to "recognize outstanding contributions to fluid dynamics" and to honour Otto Laporte . It was established as the Otto Laporte Memorial Lectureship by the APS Division of Fluid Dynamics in 1972, and became an APS award in...
of the American Physical Society
American Physical Society
The American Physical Society is the world's second largest organization of physicists, behind the Deutsche Physikalische Gesellschaft. The Society publishes more than a dozen scientific journals, including the world renowned Physical Review and Physical Review Letters, and organizes more than 20...
, and the 2003 Dirac Medal. He was also a member of the National Academy of Sciences
United States National Academy of Sciences
The National Academy of Sciences is a corporation in the United States whose members serve pro bono as "advisers to the nation on science, engineering, and medicine." As a national academy, new members of the organization are elected annually by current members, based on their distinguished and...
.
Kraichnan married twice and has a son, John Kraichnan, by his first wife, Carol Gebhardt. He is also survived by his second wife, Judy Moore-Kraichnan, an artist and photographer who lives in Santa Fe. New Mexico
Work
In the 1950s, his work was focused on quantum field theoryQuantum field theory
Quantum field theory provides a theoretical framework for constructing quantum mechanical models of systems classically parametrized by an infinite number of dynamical degrees of freedom, that is, fields and many-body systems. It is the natural and quantitative language of particle physics and...
and the quantum mechanical
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...
many-body problem
Many-body problem
The many-body problem is a general name for a vast category of physical problems pertaining to the properties of microscopic systems made of a large number of interacting particles. Microscopic here implies that quantum mechanics has to be used to provide an accurate description of the system...
, developing starting in 1957 a method for finding a self-consistent formulation for many-body field theories, N-random-coupling-models, in which N copies of a microscopic theory are coupled together in a random way.
Following earlier work of Andrei Kolmogorov (1941), Lars Onsager
Lars Onsager
Lars Onsager was a Norwegian-born American physical chemist and theoretical physicist, winner of the 1968 Nobel Prize in Chemistry.He held the Gibbs Professorship of Theoretical Chemistry at Yale University....
(1945), Werner Heisenberg
Werner Heisenberg
Werner Karl Heisenberg was a German theoretical physicist who made foundational contributions to quantum mechanics and is best known for asserting the uncertainty principle of quantum theory...
(1948), Carl Friedrich von Weizsäcker
Carl Friedrich von Weizsäcker
Carl Friedrich Freiherr von Weizsäcker was a German physicist and philosopher. He was the longest-living member of the research team which performed nuclear research in Germany during the Second World War, under Werner Heisenberg's leadership...
and others on the statistical theory of Turbulence, Kraichnan developed a field-theoretic approach to fluid flow in 1957 derived from approaches to the quantum many-body problem--- the Direct Interaction Approximation. In 1964/5, he recast this approach in the Lagrangian picture , discovering a scaling correction which he had earlier incorrectly ignored. The statistical theory of turbulence in viscous liquids describes the fluid flow by a scale-invariant distribution of the velocity field, which means that the typical size of the velocity as a function of wavenumber is a power-law. In steady state, larger scale eddies at long wavelengths disintegrate into smaller ones, dissipating their energy into smaller length scales. This type of dissipation is not caused by friction on the molecular level, but by the nonlinear effects of the Navier Stokes equations. In the final stages of the energy cascade, at the smallest length scales, the viscosity becomes important and the energy dissipates into heat.
Kraichnan developed his turbulence theories over many decades and was one of the prominent American theorists in this area. From 1967 onwards, he maintained that for two-dimensional turbulence energy does not only dissipate itself from large scales (determined by the size of obstacles in the flow) to smaller ones as it does in three dimensions, but conversely that smaller fluctuations can increase in size. This theory is called the inverse Energy Cascade, and it is especially applicable to oceanography and meteorology, since flows on the surface of the earth are approximately two-dimensional. The theory was tested and confirmed in the 1980s by data gathered from weather balloons.
Also influential was a 1994 paper which presented an exactly solvable turbulence model, now called the Kraichnan model. This model predicts exactly computable anomalous scaling exponents for the advection
Advection
Advection, in chemistry, engineering and earth sciences, is a transport mechanism of a substance, or a conserved property, by a fluid, due to the fluid's bulk motion in a particular direction. An example of advection is the transport of pollutants or silt in a river. The motion of the water carries...
of a passive scalar field, like the concentration of a dye injected into the fluid which does not diffuse but moves with the fluid along the flow lines.
Even as a student, Kraichnan was busily investigating the general theory of relativity
General relativity
General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...
, and his research won the prestigious Westinghouse Science Competition for students. He rewrote this work for his Bachelor thesis at MIT in 1947, titled "Quantum Theory of the Linear Gravitational Field" . Following an approach that was echoed by Suraj N. Gupta
Suraj N. Gupta
Suraj N. Gupta is an Indian-born American theoretical physicist, notable for his contribution to quantum field theory.-Education and career:...
, Richard Feynman
Richard Feynman
Richard Phillips Feynman was an American physicist known for his work in the path integral formulation of quantum mechanics, the theory of quantum electrodynamics and the physics of the superfluidity of supercooled liquid helium, as well as in particle physics...
and Steven Weinberg
Steven Weinberg
Steven Weinberg is an American theoretical physicist and Nobel laureate in Physics for his contributions with Abdus Salam and Sheldon Glashow to the unification of the weak force and electromagnetic interaction between elementary particles....
, Kraichnan showed that, under some mild secondary assumptions, the full nonlinear equations of general relativity follow from its linearized form: the quantum field theory
Quantum field theory
Quantum field theory provides a theoretical framework for constructing quantum mechanical models of systems classically parametrized by an infinite number of dynamical degrees of freedom, that is, fields and many-body systems. It is the natural and quantitative language of particle physics and...
of a massless spin 2 particle, the graviton, coupled to the stress-energy tensor. The full nonlinear equations emerge when the energy-momentum of the gravitons themselves are included in the stress-energy tensor in a unique self-consistent way.