A connection between the Camassa{endash}Holm equations and turbulent flows in channels and pipes
- Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)
- Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico (United States)
- Departments of Mathematics, Mechanical and Aerospace Engineering, University of California, Irvine, California 92697 (United States)
In this paper we discuss recent progress in using the Camassa{endash}Holm equations to model turbulent flows. The Camassa{endash}Holm equations, given their special geometric and physical properties, appear particularly well suited for studying turbulent flows. We identify the steady solution of the Camassa{endash}Holm equation with the mean flow of the Reynolds equation and compare the results with empirical data for turbulent flows in channels and pipes. The data suggest that the constant {alpha} version of the Camassa{endash}Holm equations, derived under the assumptions that the fluctuation statistics are isotropic and homogeneous, holds to order {alpha} distance from the boundaries. Near a boundary, these assumptions are no longer valid and the length scale {alpha} is seen to depend on the distance to the nearest wall. Thus, a turbulent flow is divided into two regions: the constant {alpha} region away from boundaries, and the near wall region. In the near wall region, Reynolds number scaling conditions imply that {alpha} decreases as Reynolds number increases. Away from boundaries, these scaling conditions imply {alpha} is independent of Reynolds number. Given the agreement with empirical and numerical data, our current work indicates that the Camassa{endash}Holm equations provide a promising theoretical framework from which to understand some turbulent flows. {copyright} {ital 1999 American Institute of Physics.}
- OSTI ID:
- 351861
- Journal Information:
- Physics of Fluids (1994), Vol. 11, Issue 8; Other Information: PBD: Aug 1999
- Country of Publication:
- United States
- Language:
- English
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