We conduct long-time simulations with a Hamiltonian particle-mesh method for ideal fluid flow, to determine the statistical mean vorticity field of the discretization. Lagrangian and Eulerian statistical models are proposed for the discrete dynamics, and these are compared against numerical experiments. The observed results are in excellent agreement with the theoretical models, as well as with the continuum statistical mechanical theory for ideal fluid flow developed by Ellis et al. (2002). In particular the results verify that the apparently trivial conservation of potential vorticity along particle paths within the HPM method significantly influences the mean state. As a side note, the numerical experiments show that a nonzero fourth moment of potential vorticity can influence the statistical mean.
Additional Metadata
Keywords Conservative discretizations, Statistical mechanics, Geometric numerical integration, Quasigeostrophic flow, Geophysical fluid dynamics
Publisher Elsevier
Persistent URL dx.doi.org/10.1016/j.jcp.2009.12.012
Journal Journal of Computational Physics
Project Symplectic Integration of Atmospheric Dynamics: Long-term Statistical Accuracy for Ensemble Climate Simulations
Citation
Dubinkina, S, & Frank, J.E. (2010). Statistical relevance of vorticity conservation with the Hamiltonian particle-mesh method. Journal of Computational Physics, 229(7), 2634–2648. doi:10.1016/j.jcp.2009.12.012