ANZIAM J. 46(E) pp.C704--C718, 2005.
The statistical dynamics of turbulent Rossby wave flow over topography
T. J. O'Kane | J. S. Frederiksen |
Abstract
The statistical dynamics of Rossby wave turbulence is examined by comparing direct numerical simulation of the vorticity form of the 2-D Navier--Stokes equation with a non-Markovian statistical closure theory for inhomogeneous flow over mean topography. The quasi-diagonal direct interaction approximation closure theory is formulated for the interaction of mean fields, Rossby waves and inhomogeneous turbulence over topography on a generalized b-plane. The competing effects of nonlinear waves at the large scales and fully developed turbulence at the small scales is examined by comparing closure theory with ensemble averaged results from direct numerical simulation at resolution k=48 for circularly truncated wavenumber space. This work builds on the low resolution b-plane studies of Frederiksen and O'Kane (2005) and extends the high resolution f-plane studies of O'Kane and Frederiksen (2004) to incorporate waves. We also examine the performance of a computationally efficient restart or cumulant update procedure at moderate Reynolds number in the presence of waves.
Download to your computer
- Click here for the PDF article (207 kbytes) We suggest printing 2up.
- Click here for its BiBTeX record
Authors
- T. J. O'Kane
- CSIRO Atmospheric Research, Aspendale, Australia. mailto:Terence.O'Kane@csiro.au
- J. S. Frederiksen
- CSIRO Atmospheric Research, Aspendale, Australia. mailto:Jorgen.Frederiksen@csiro.au
Published July 27, 2005. ISSN 1446-8735
References
- Frederiksen, J. S. 1999 Subgrid-scale parameterizations of eddy-topographic force, eddy viscosity, and stochastic backscatter for flow over topography. J. Atmos. Sci. 56, 1481--1494.
- Frederiksen, J. S., & O'Kane, T. J. 2005 Inhomogeneous closure and statistical mechanics for Rossby wave turbulence over topography J. Fluid Mech., In press
- Kraichnan, R. H. 1959a The structure of isotropic turbulence at very high Reynolds numbers. J. Fluid Mech. 5, 497--543.
- Kraichnan, R. H. 1972 Test-field model for inhomogeneous turbulence. J. Fluid Mech. 56, 287--304.
- O'Kane, T. J., & Frederiksen, J. S. 2003 Integro-differential closure equations for inhomogeneous turbulence. ANZIAM J. 44(E), C569--C589. http://anziamj.austms.org.au/V44/CTAC2001/Okan
- O'Kane, T. J., & Frederiksen, J. S. 2004 A tractable inhomogeneous closure theory for flow over mean topography. ANZIAM J. 45(E), C135--C148. http://anziamj.austms.org.au/V45/CTAC2003/Okan
- O'Kane, T. J., & Frederiksen, J. S. 2004 The QDIA and regularized QDIA closures for inhomogeneous turbulence over topography. J. Fluid Mech. 504, 133--165. http://dx.doi.org/10.1017/S0022112004007980