Camassa-Holm Equations as a Closure Model for Turbulent Channel and Pipe Flow

Shiyi Chen,1 Ciprian Foias,1,2 Darryl D. Holm,1 Eric Olson,1,2 Edriss S. Titi,3,4,5 and Shannon Wynne3,5 1Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 2Department of Mathematics, Indiana University, Bloomington, Indiana 47405 3Department of Mathematics, University of California, Irvine, California 92697 4Department of Mechanical and Aerospace Engineering, University of California, Irvine, California 92697 5Institute for Geophysics and Planetary Physics, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (Received 15 April 1998; revised manuscript received 9 September 1998)