Properties of the conditionally filtered equations: Conservation, normal modes, and variational formulation
dc.contributor.author | Thuburn, J | |
dc.contributor.author | Vallis, G | |
dc.date.accessioned | 2018-04-09T14:44:52Z | |
dc.date.issued | 2018-04-10 | |
dc.description.abstract | Conditionally filtered equations have recently been proposed as a basis for modelling the atmospheric boundary layer and convection. Conditional filtering decomposes the fluid into a number of categories or components, such as convective updrafts and the background environment, and derives governing equations for the dynamics of each component. Because of the novelty and unfamiliarity of these equations, it is important to establish some of their physical and mathematical properties, and to examine whether their solutions might behave in counter-intuitive or even unphysical ways. It is also important to understand the properties of the equations in order to develop suitable numerical solution methods. The conditionally filtered equations are shown to have conservation laws for mass, entropy, momentum or axial angular momentum, energy, and potential vorticity. The normal modes of the conditionally filtered equations include the usual acoustic, inertio-gravity, and Rossby modes of the standard compressible Euler equations. In addition, they posses modes with different perturbations in the different fluid components that resemble gravity modes and inertial modes but with zero pressure perturbation. These modes make no contribution to the total filter-scale fluid motion, and their amplitude diminishes as the filter scale diminishes. Finally, it is shown that the conditionally filtered equations have a natural variational formulation, which can be used as a basis for systematically deriving consistent approximations. | en_GB |
dc.description.sponsorship | We are grateful to two anonymous reviewers for their constructive comments on an earlier version of this paper. This work was funded by the Natural Environment Research Council under grant NE/N013123/1 as part of the ParaCon programme. | en_GB |
dc.identifier.citation | Published online 10 April 2018 | en_GB |
dc.identifier.doi | 10.1002/qj.3307 | |
dc.identifier.uri | http://hdl.handle.net/10871/32396 | |
dc.language.iso | en | en_GB |
dc.publisher | Wiley / Royal Meteorological Society | en_GB |
dc.rights | © 2018 The Authors. Quarterly Journal of the Royal Meteorological Society published by John Wiley & Sons Ltd on behalf of the Royal Meteorological Society. This is an open access article under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/), which permits use, distribution and reproduction in any medium, provided the original work is properly cited. | |
dc.subject | Approximate equations | en_GB |
dc.subject | Conditional average | en_GB |
dc.subject | Convection | en_GB |
dc.subject | Hamilton’s principle | en_GB |
dc.title | Properties of the conditionally filtered equations: Conservation, normal modes, and variational formulation | 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 |
dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ |
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Except where otherwise noted, this item's licence is described as © 2018 The Authors. Quarterly Journal of the Royal Meteorological Society published by John Wiley & Sons Ltd on behalf of the Royal Meteorological Society.
This is an open access article under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/), which permits use, distribution and reproduction in any medium, provided the original work is properly cited.