dc.contributor.author | Bell, MJ | |
dc.contributor.author | Peixoto, PS | |
dc.contributor.author | Thuburn, J | |
dc.date.accessioned | 2016-10-26T09:21:07Z | |
dc.date.issued | 2016-10-21 | |
dc.description.abstract | The linear stability of two well known energy and enstrophy conserving schemes for
the vector invariant hydrostatic primitive equations is examined. The problem is analysed for a
stably stratified Boussinesq fluid on an f -plane, with a constant velocity field, in height and
isopycnal coordinates, by separation of variables into vertical normal modes and a linearised
form of the shallow water equations (SWEs). As found by [Hollingsworth
~al.(1983)Hollingsworth, Kallberg, Renner and Burridge], (HKRB hereafter) the schemes are
linearly unstable in height coordinate models, due to a non-cancellation of terms in the
momentum equations. The schemes with the modified formulations of the kinetic energy
proposed by HKRB are shown to have Hermitain stability matrices and hence to be stable to all
perturbations. All perturbations in isopycnal models are also shown to be neutrally stable, even
with the original formulations for kinetic energy. Analytical expressions are derived for the
smallest equivalent depths obtained using Charney-Phillips and Lorenz vertical grids, which
show that the Lorenz grid has larger growth rates for the unstable schemes than the CharneyPhillips
grid. Test cases are proposed for assessing the stability of new numerical schemes using
the SWEs. | en_GB |
dc.description.sponsorship | We gratefully acknowledge inputs from Nicolas Ducousso,
Gurvan Madec, Julien le Sommer, David Storkey, Andy
White and Nigel Wood. Bell was supported by the
Joint UK DECC/Defra Met Office Hadley Centre Climate
Programme (GA01101), Peixoto acknowledges the Sao
Paulo Research Foundation (FAPESP), under the grant
number 2014/10750-0 and Thuburn was supported by the
Natural Environment Research Council under grant number
NE/K006762/1. | en_GB |
dc.identifier.citation | Vol. 143 (702), pp. 563-581 | en_GB |
dc.identifier.doi | 10.1002/qj.2950 | |
dc.identifier.uri | http://hdl.handle.net/10871/24089 | |
dc.language.iso | en | en_GB |
dc.publisher | Wiley | en_GB |
dc.rights.embargoreason | Publisher Policy | en_GB |
dc.subject | Hollingsworth instabilities | en_GB |
dc.subject | vector invariant momentum equations | en_GB |
dc.subject | shallow water equations | en_GB |
dc.subject | separation of variables | en_GB |
dc.subject | energy and enstrophy conservation | en_GB |
dc.title | Numerical instabilities of vector invariant momentum equations on rectangular C-grids | en_GB |
dc.type | Article | en_GB |
dc.identifier.issn | 0035-9009 | |
dc.description | This is the author accepted manuscript. The final version is available from Wiley via the DOI in this record | en_GB |
dc.identifier.journal | Quarterly Journal of the Royal Meteorological Society | en_GB |
refterms.dateFOA | 2017-10-20T23:00:00Z | |