Energy conserving and potential-enstrophy dissipating schemes for the shallow water equations

To incorporate potential enstrophy dissipation into discrete shallow water equations with no or arbitrarily small energy dissipation, a family of finite-difference schemes have been derived with which potential enstrophy is guaranteed to decrease while energy is conserved (when the mass flux is nond...

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Bibliographic Details
Published in:Monthly weather review 1990-10, Vol.118 (10), p.1960-1969
Main Authors: Arakawa, Akio, Hsu, Yueh-Jiuan G.
Format: Article
Language:English
Subjects:
Convection, turbulence, diffusion. Boundary layer structure and dynamics
Earth, ocean, space
Exact sciences and technology
External geophysics
Fluid Mechanics And Heat Transfer
Meteorology
Online Access:Get full text
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Summary:To incorporate potential enstrophy dissipation into discrete shallow water equations with no or arbitrarily small energy dissipation, a family of finite-difference schemes have been derived with which potential enstrophy is guaranteed to decrease while energy is conserved (when the mass flux is nondivergent and time is continuous). Among this family of schemes, there is a member that minimizes the spurious impact of infinite potential vorticities associated with infinitesimal fluid depth. The scheme is, therefore, useful for problems in which the free surface may intersect with the lower boundary.
ISSN:0027-0644
1520-0493
DOI:10.1175/1520-0493(1990)118<1960:ecaped>2.0.co;2