Journal ofStatisticalPhysics, VoL 19, No. 5, 1978 Cascade Robert M. Model of Fully Developed Turbulence Kerr 1 and Erie D. Siggia 2,s Received June 6, 1978 A simple system of quadratically nonlinear equations representing a hierarchy of frequency scales is derived from a cutoff version of Burgers" equation. When forced, the model system reproduces a number of quali- tative features of fully developed turbulence. In equilibrium, the model exhibits, in addition to the energy, an extensive isolating integral of the motion that is cubic in the velocity. KEY WORDS: Intermittency; fully developed turbulence; cascade model; Burgers" equation. 1. INTRODUCTION Kolmogorov's phenomenological theory for the energy spectrum in a turbulent fluid in three dimensions is perhaps the single most successful theoretical attempt to comprehend fully developed turbulence. (1) Neverthe- less it fails to account for certain fluctuation effects (" intermittency ") that are seen experimentally in three dimensions3 2) Furthermore, it is formulated in such general terms that it would appear to apply to a number of simpler models, such as Burgers' equationY ) This work was aided by a direct grant of computer time from NCAR. This work was in part supported by the National Science Foundation under Grant No. ENG 74- 08501A02. 1 Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York. 2 Laboratory of Atomic and Solid State Physics and Laboratory of Nuclear Studies, Cornell University, Ithaca, New York, and National Center for Atmospheric Research, Boulder, Colorado. a Permanent address: Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York. 543 0022-4715178II100-0543505.00/0 91978PlenumPublishingCorporation