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

Shiyi Chen; Ciprian Foias; Darryl D. Holm; Eric Olson; Edriss S. Titi; Shannon Wynne

doi:10.1103/PhysRevLett.81.5338

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

Shiyi Chen, Ciprian Foias, Darryl D. Holm, Eric Olson, Edriss S. Titi, and Shannon Wynne

Phys. Rev. Lett. 81, 5338 – Published 14 December 1998

Abstract

We propose the viscous Camassa-Holm equations as a closure approximation for the Reynolds-averaged equations of the incompressible Navier-Stokes fluid. This approximation is tested on turbulent channel and pipe flows with steady mean. Analytical solutions for the mean velocity and the Reynolds shear stress are consistent with experiments in most of the flow region.

Received 15 April 1998

DOI:https://doi.org/10.1103/PhysRevLett.81.5338

Authors & Affiliations

Shiyi Chen¹, Ciprian Foias^1,2, Darryl D. Holm¹, Eric Olson^1,2, Edriss S. Titi^3,4,5, and Shannon Wynne^3,5

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