Identification

Title

A potential enstrophy and energy conserving scheme for the shallow-water equations extended to generalized curvilinear coordinates

Abstract

An energy and potential enstrophy conserving finite-difference scheme for the shallow-water equations is derived in generalized curvilinear coordinates. This is an extension of a scheme formulated by Arakawa and Lamb for orthogonal coordinate systems. The starting point for the present scheme is the shallow-water equations cast in generalized curvilinear coordinates, and tensor analysis is used to derive the invariant conservation properties. Preliminary tests on a flat plane with doubly periodic boundary conditions are presented. The scheme is shown to possess similar order-of-convergence error characteristics using a non-orthogonal coordinate compared to Cartesian coordinates for a nonlinear test of flow over an isolated mountain. A linear normal mode analysis shows that the discrete form of the Coriolis term provides stationary geostrophically balanced modes for the nonorthogonal coordinate and no unphysical computational modes are introduced. The scheme uses centered differences and averages, which are formally second-order accurate. An empirical test with a steady geostrophically balanced flow shows that the convergence rate of the truncation errors of the discrete operators is second order. The next step will be to adapt the scheme for use on the cubed sphere, which will involve modification at the lateral boundaries of the cube faces.

Resource type

document

Resource locator

Unique resource identifier

code

http://n2t.net/ark:/85065/d7vh5qn5

codeSpace

Dataset language

eng

Spatial reference system

code identifying the spatial reference system

Classification of spatial data and services

Topic category

geoscientificInformation

Keywords

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keyword value

Text

originating controlled vocabulary

title

Resource Type

reference date

date type

publication

effective date

2016-01-01T00:00:00Z

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Dataset reference date

date type

publication

effective date

2017-03-01T00:00:00Z

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Conformity

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Limitations on public access

None

Responsible organisations

Responsible party

contact position

OpenSky Support

organisation name

UCAR/NCAR - Library

full postal address

PO Box 3000

Boulder

80307-3000

email address

opensky@ucar.edu

web address

http://opensky.ucar.edu/

name: homepage

responsible party role

pointOfContact

Metadata on metadata

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