Large-scale Weather Prediction Research Articles

On hydrostatic flows in isentropic coordinates

The hydrostatic primitive equations of motion which have been used in large-scale weather prediction and climate modelling over the last few decades are analysed with variational methods in an isentropic Eulerian framework. The use of material isentropic coordinates for the Eulerian hydrostatic equations is known to have distinct conceptual advantages since fluid motion is, under inviscid and statically stable circumstances, confined to take place on quasi-horizontal isentropic surfaces. First, an Eulerian isentropic Hamilton's principle, expressed in terms of fluid parcel variables, is therefore derived by transformation of a Lagrangian Hamilton's principle to an Eulerian one. This Eulerian principle explicitly describes the boundary dynamics of the time-dependent domain in terms of advection of boundary isentropes sB; these are the values the isentropes have at their intersection with the (lower) boundary. A partial Legendre transform for only the interior variables yields an Eulerian ‘action’ principle. Secondly, Noether's theorem is used to derive energy and potential vorticity conservation from the Eulerian Hamilton's principle. Thirdly, these conservation laws are used to derive a wave-activity invariant which is second-order in terms of small-amplitude disturbances relative to a resting or moving basic state. Linear stability criteria are derived but only for resting basic states. In mid-latitudes a time- scale separation between gravity and vortical modes occurs. Finally, this time-scale separation suggests that conservative geostrophic and ageostrophic approximations can be made to the Eulerian action principle for hydrostatic flows. Approximations to Eulerian variational principles may be more advantageous than approximations to Lagrangian ones because non-dimensionalization and scaling tend to be based on Eulerian estimates of the characteristic scales involved. These approximations to the stratified hydrostatic formulation extend previous approximations to the shallow- water equations. An explicit variational derivation is given of an isentropic version of Hoskins & Bretherton's model for atmospheric fronts.

Dispersion processes in large‐scale weather prediction. By N. Phillips. WMO Bulletin no. 700, 1990. Pp. 126. ISBN 92‐63‐10700‐9

Quarterly Journal of the Royal Meteorological SocietyVolume 120, Issue 515 p. 231-232 Review Dispersion processes in large-scale weather prediction. By N. Phillips. WMO Bulletin no. 700, 1990. Pp. 126. ISBN 92-63-10700-9 G. J. Shutts, G. J. ShuttsSearch for more papers by this author G. J. Shutts, G. J. ShuttsSearch for more papers by this author First published: January 1994 Part A https://doi.org/10.1002/qj.49712051515AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat No abstract is available for this article. Volume120, Issue515January 1994 Part APages 231-232 RelatedInformation

A barotropic planetary boundary layer

The temperature and wind profiles in the planetary boundary layer (PBL) are investigated. Assuming stationary and homogeneous conditions, the turbulent state in the PBL is uniquely determined by the external Rossby number and the stratification parameters. In this study, a simple two-layer barotropic model is proposed. It consists of a surface (SL) and overlying Ekman-type layer. The system of dynamic and heat transfer equations is closed usingK theory. In the SL, the turbulent exchange coefficient is consistent with the results of similarity theory while in the Ekman layer, it is constant. Analytical solutions for the wind and temperature profiles in the PBL are obtained. The SL and thermal PBL heights are properly chosen functions of the stratification so that from the solutions for wind and temperature, the PBL resistance laws can be easily deduced. The internal PBL characteristics necessary for the calculation (friction velocity, angle between surface and geostrophic winds and internal stratification parameter) are presented in terms of the external parameters. Favorable agreement with experimental data and model results is demonstrated. The simplicity of the model allows it to be incorporated in large-scale weather prediction models as well as in the solution of various other meteorological problems.