Early work of Andrey Kolmogorov, Lars Onsager, and Werner Heisenberg established that it is productive to describe a turbulent fluid with a statistically self-similar velocity field at length scales shorter than the driving force responsible for the flow, but longer than the length scale at which the viscosity allows energy to dissipate. In this regime, energy was assumed to always flow from large length scales to small ones. Among his other achievements in the field, Kraichnan established that in two dimensional fluid flows the energy cascade goes in the opposite direction--- from small length scales to large ones. Some of his work centered on perturbative studies of statistical field theories of turbulence, which led to a rapid growth in the field in the 1960's and 1970's.
In gravitation theory, Kraichnan was the first to note that General Relativity is the unique self-consistent equation of a spin two particle coupled to a conserved energy-momentum tensor, where the nonlinearities are understood as the graviton responding to its own stress energy. This point of view was later popularized by Richard Feynman .
He was the recipient of the 1993 Otto Laporte Award. and the 2003 Dirac medal.